The methods disclosed comprise the linehaul optimization algorithm which is a hybrid algorithm incorporating the basic structure of the Hungarian Assignment algorithm or equivalent and an improvement heuristic. However, in this particular case there is not a direct application of the existing, well-known Hungarian Assignment algorithm or equivalent in conjunction with a heuristic. The structure of the assignment model being used here is based on the Hungarian Assignment algorithm or equivalent but has been revised and enhanced to identify systematically (by using grouping) a number of equivalent optimal solutions (that give the same optimal, minimum cost for a particular iteration). A heuristic is then used to identify the ‘best’ optimal solution, of the many identified, that would contribute the most incremental cost reduction in future iterations of the heuristic.

The efficiency of transportation operations is one of the factors having a significant effect on the country's economic growth. A linehaul operation, one of the biggest contributors to the total operating cost of a trucking company, involves moving full loads of less than unit load or full unit load shipments using owner-operator and/or company units.
A review of the prior art revealed that for an optimization procedure to be successful, the following steps have to be executed in sequential order:                (1) Problem definition,        (2) Model development of the problem, and        (3) Solution algorithm development for the model.
The problem must be defined in the most appropriate manner such that it meets the practical requirements of the real-world problem. This ensures that, when the model is developed, it is a more accurate mathematical representation of the problem. The algorithm developed to meet the requirements of the model can be an existing algorithm, a modified existing algorithm, or a new algorithm developed specifically to solve the model. Since algorithms are usually not developed to solve a specific problem, they require significant modification to address specific operational requirements. If the problem to be solved is a unique problem and cannot be addressed by any of the existing algorithms, it is necessary to develop a new algorithm to meet its requirements.
Some of the existing modeling and solution approaches from recent research that are relevant to linehaul operations are discussed in the following sections of this chapter. There are also some commercially available software packages intended to assist in modeling transportation operation problems, and/or finding a solution to the modeled problem. The advantages and disadvantages of these packages are also discussed in the Commercial Modeling Packages section of this chapter. Although considerable research has been completed in the transport operations area, the scale, nature, and complexity of the current linehaul problem addressed in the present invention is significantly different from ones that have been studied so far and reported in prior art.
The linehaul planning problem and the Vehicle Routing Problem (VRP) in general are non-deterministic polynomial time hard (NP-hard) combinatorial optimization problems for which no efficient algorithms are known that provide a global optimum solution. The solution approaches to NP-hard combinatorial problems can be grouped into two categories, namely exact solution approaches and heuristic solution approaches. The exact solution approach looks into almost every possibility to find the optimum solution and is useful for problems of relatively small size. Heuristic algorithms do not indicate how good the result is in relation to the global optimum, but they are the most practical choice for solving large problems because of the efficiency gains and improvements that they can potentially make.
The Traveling Salesman Problem (TSP) is one of the best known problems in combinatorial optimization (Cook et al., 1998). TSP is a sub-problem of the VRP (Lawler et al., 1992). VRP can have a larger set of solution possibilities, depending on the nature of the problem. The TSP can be described as having N destinations, and the cost, Cij to travel from destination i to j. A salesman (vehicle) starts from the depot to visit each destination once and return back to the depot. The problem is to find the optimal route and the destination visiting order that would yield the minimum total travel cost. If the entire set of solutions were enumerated, the number of calculations would be N! (Taniguchi et al., 2001). Table 2 shows the rapid growth of computational time for solving TSP when N, the number of destinations (customers), increases. In this example, a 10 gigahertz (GHz) processor with basic computation time of 10−10 seconds was used. In an enumeration method, one step may take several computations, but to be conservative, it was treated as if it would take the same time as for one computation. As the following table shows, when N increases from 10 to 50 destinations, computation time to find an exact solution increases from 0.00036 seconds to 9.64*1037 billion years:
Sample SizeComputation Time100.00036seconds207.7years30841111billion years402.59 * 1021billion years509.64 * 1037billion years
Clarke and Wright (1964) developed the earliest heuristic algorithm (that is the Clarke-Wright heuristic algorithm) to solve the VRP. Significant research done to solve the VRP has helped in the development of many heuristic algorithms, which are now commonly used, such as Tabu Search (TS), Simulated Annealing (SA), Genetic Algorithms (GA), and Repeated Descent (RD). Gendreau et al. (1997) applied several heuristics to the VRP and their findings were that the GA, SA, and TS techniques performed significantly well in VRP compared to other algorithms. Wright and Marett (1996) compared the performance of RD, SA, and TS on the TSP and TS outperformed both SA and RD.
Taniguchi et al. (1998) compared the performance of the GA, SA, and TS when applied to the VRP, and concluded that the TS reached the best known solution with the shortest computation time. Reviews on ten of the most common TS heuristics for the VRP with their main features of neighbourhood structures, short term memory, long term memory, and intensification can be found in one of the most recent surveys conducted by Cordeau and Laporte (2002).
The classical VRP is to determine the routes and service order of customers with known demands from a central depot. Although classical VRP models and algorithms cannot be applied to solve linehaul scheduling problems, due to some similarities in the nature of their operations, a survey of the literature pertaining to classical VRP is also included in this chapter. This was done for the purpose of ascertaining what scholars have done to handle similar situations in this subject. It also revealed an understanding of current active research modeling approaches and solution algorithms.
A comprehensive literature survey on the classical VRP and some of its variations was made by Fisher (1995), where he categorized VRP methods into three generations. The first generation consisted of simple heuristics developed in the 60's and 70's, which were mainly based on local search or sweep methods. The second generation included mathematical programming based heuristics (near-optimization algorithms), which differ from normal heuristics in that they include the generalized assignment problems and set partitioning to approximate the VRP. The third and the last generation is the one currently being studied intensively and includes exact optimization algorithms and artificial intelligence methods such as TS, GA, and SA. Christie and Satir (2004) reviewed several existing case studies and found that a 10% to 30% reduction in operational costs is possible through VRP optimization for P & D operations. Satir (2003) analyzed the P & D operations (at a terminal) of a major trucking company in Atlantic Canada, and compared the potential efficiency gains of implementing an optimization system. The results of the case study showed that operational costs could be reduced by as much as 50%.
The classical VRP is not applicable (without additional constraints and considerable modification) to real-world transportation operation problems. One of the problems closest in nature to the classical VRP is that of parcel P & D. In most P & D operations vehicles have various fixed capacities and can serve customers (with varying demands) only within this capacity. This type of problem is referred to as the Capacitated VRP (CVRP) in literature. In most real-world transportation problems, customers have certain time windows within which they have to be served by a fleet of vehicles of varying capacities. This type of CVRP with time windows (TW) is known as VRPTW. The VRPTW has many practical applications such as in LTL P & D from a central depot or multiple depots. Tan et al. (2000) investigated various third generation heuristic methods such as TS, SA, and GA to solve the VRPTW.
Although the classical VRP and some of its variations have been studied extensively in literature, VRP with FTL (VRPFTL) has received relatively less attention in literature. The closest VRP variations to VRPFTL are the multi-depot vehicle scheduling problem with time windows (MDVSPTW) and the multi-trip vehicle routing and scheduling problem (MTVRSP), which have been studied comparatively more. The main difference between VRPFTL and MDVSPTW is that while VRPFTL has one FTL demand per trip (one customer), MDVSPTW can have one or more customer demands to fill the truck per trip. Brandao (1997) points out that the MTVRSP has additional constraints to the VRPTW such as a vehicle can make more than one trip, vehicle's capacity is considered in terms of both volume and weight, the access to some customers is restricted to some vehicles, and driver's schedule must comply with the driving regulations. Desaulniers et al. (1998) published a paper on MDVSPTW and waiting costs, which bears some similarities to the problem addressed in this present invention. A literature survey was also made by Desrosiers et al. (1995) for multi-depot VRP related problems. A recent VRPFTL paper published by Arunapuram et al. (2003) introduced new techniques that were intended to solve such problems with exact solutions, which use a branch-and-bound algorithm to solve an integer-programming formulation of the VRP.
Yang et al. (2004) published a paper which considered various costs associated with empty miles, delayed completion times, and job rejection when using real time information to improve productivity. Liu et al. (2003) developed a heuristic algorithm to determine a mixed truck delivery system that allows both hub-and-spoke and direct shipment delivery modes. Smilowitz et al. (2003) studied the possible integration of longhaul operations for package delivery services, which has similar context to some of the components of the problem addressed in the present invention.
Trucking operations consist of P & D and linehaul operations. The classical VRP is applicable primarily to P & D operations. Although a considerable amount of research on the classical VRP exists in literature, relatively less research has been done on vehicle scheduling and planning for linehaul operations. Planning and scheduling of transportation operations has potential applications in the rail, maritime, trucking, and airline modes of transportation. Some of the real-world problems, models proposed, applications, and implementation benefits pertaining to planning and scheduling in literature are discussed in this section.
Linehaul planning is more challenging than the typical VRP in that the fleet of vehicles has to satisfy each terminal's varying demands from every other terminal, whereas in the classical VRP, it has to satisfy customer demands only from a central terminal. One of the most similar problems to linehaul planning is that of airline planning and scheduling. Significant research has been undertaken in this area, and OR has had a significant impact on the airline industry. Clarke and Smith (2004) point out that American Airlines had an estimated cost savings of approximately $18 million USD per year (relative to previously used enumeration methods) by implementing an optimization-based crew pairing system in 1989. Cook (2000) claims that American Airlines testified that over $500 million was generated annually in incremental profits due to their optimized schedule planning system. In a similar manner, when the Delta Airlines first implemented their fleet assignment module in 1992, the planning group reported an approximate cost savings of more than $100,000 USD per day (Subramaniam, 1994). These cost savings increased as planners gained more experience and confidence with the module, and reached an estimated $200,000 USD per day in late 1993. Ryan et al (2001) reported not only an increase in savings of more than $15,655,000 NZ per year in crew scheduling costs at Air New Zealand, but also an increase in crew member satisfaction.
Many of the problems found in maritime, railway, and airline transportation operations are based on multi-commodity flow problems. A multi-commodity flow problem is defined in the Algorithms and Theory of Computation Handbook as "a maximum-flow problem (finding the maximum flow between any two vertices of a directed graph) involving multiple commodities, in which each commodity has an associated demand and source-sink pairs".
Barnhart et al. (1995) published a partitioning solution procedure to address large-scale multi-commodity flow problems with many commodities. Barnhart et al. (2000) presented a model and iterative solution approach to solve the problem of determining the type of aircraft to assign to each flight and the exact departure time of each flight, given the set of flights with their time windows for a large U.S airline. It should be noted that the process of fleet assignment in airline operations is very similar to tractor assignments in trucking operations, subject to different operational and regulatory constraints.
Barnhart, Hane, and Vance (2000) proposed a branching rule to find a heuristic solution and compared branch-and-price and branch-and-price-and-cut methods to find optimal solutions for highly capacitated problems, specific to telecommunication applications. Barnhart et al. (2002) proposed a new formulation and solution approach that captures network effects and involves the profit maximizing assignment of aircraft types to flight legs.
The general framework for aircraft and crew schedule and planning is given in (Barnhart, 2004). Although decomposing the problem into four subproblems and optimizing them individually would yield a less efficient solution than an overall optimization approach, it is necessary to decompose problems of large size such as linehaul problems in a similar manner to obtain a practical solution in a feasible time.
Toth (2004) stresses the need to undertake planning activities in an efficient way for railway transportation operations and the importance of using computer-aided tools to improve the planning ability of railway systems. He points out some of the problems arising in railway optimization to be line planning, platforming, shunting, locomotive assignment and scheduling, crew scheduling, and train timetabling. In particular, the train timetabling problem, which deals with train scheduling and dispatching, is of similar nature to linehaul planning. Caprara et al. (2002) proposed a graph theoretic formulation to model and solve the train timetabling problem using a directed multigraph in which nodes correspond to departures or arrivals at a certain station at a given instant.
It is also beneficial to understanding the recent research in maritime transportation, since ship routing and scheduling problems are related to linehaul planning problems. Christiansen et al. (2004) reviewed the current status of ship routing and scheduling based on literature published in the last decade. They presented perspectives regarding future developments and use of optimization-based decision-support systems for ship routing and scheduling. They also examined tactical and operational fleet planning operations and consider problems that comprise various ship routing and scheduling aspects. Hooghiemstra et al. (1999) proposed a model for a real ship planning problem, which is a combined inventory management problem and a routing problem with time windows. They also discuss model adjustments to the proposed model to decompose the problem into ship routine and inventory management subproblems. Flatberg et al. (2000) combined an iterative improvement heuristic with an exact solution approach to minimize transportation costs (while ensuring satisfactory inventory levels) within acceptable time limits. The model was for a real-world problem of transporting a single commodity between producing and consuming factories within the same company using a fleet of vessels.
Powel (1996) proposed a stochastic formulation of the dynamic assignment problem with an application to truckload motor carriers where demands arise randomly and continuously throughout the day. Powel et al. (2002) did a case study on implementing operational planning (real-time load matching) model for a trucking carrier. Powel et al. (2000) found that the value of global optimization is lost when users ignore the solution suggested by the model. Crainic and Laporte (1997) discussed some of the main issues in freight transportation operations planning and presented appropriate Operations Research models and methods, as well as computer-based planning tools. They examined the strategic, tactical, and operational decision-making levels and also reviewed significant methodological and instrumental developments in these areas.
The earliest models in freight transportation were deterministic models that captured the time staging of physical activities as against the time staging of information (Powell, 2003). Powell and Carvalho (1998) proposed the use of linear functional approximations to measure the future impact of current decisions in freight transportation planning. Godfrey and Powell (2002) found that non-linear functional approximations produced a better and more stable solution than linear approximations.
Powell et al. (2004) explained a transportation system in terms of the management of the static resources (such as terminals) and passive resources (such as people and equipment) that constrain the system. They also introduced a basic resource model for modeling resources and their attributes. Powell, Shapiro, and Simaõ (2002) formulated a large-scale driver scheduling problem as a multistage dynamic resource allocation problem for an LTL trucking application. The large scale of the problem rendered the use of commercial solvers infeasible. They demonstrated that their techniques provided high quality solutions within reasonable time limits. Powell and Topaloglu (2005) discuss the fleet management problem, which involves managing fleets of equipment to meet the customer requests that arrive randomly over time, often requiring service within a small time window.
Transportation operation problems can be grouped into point-to-point (node) routing and arc routing problems. While in node routing problems the service activity occurs at all (or at some subset of) the nodes, in arc routing problems a single vehicle or a fleet of vehicles must service all (or some subset of) the arcs (and/or edges) of a transportation network (Corberan et al. 2005). The majority of operations fall under the category of point-to-point routing, such as VRP and linehaul operations. Arc routing applications include garbage collection, snow removal, sweeping, gritting, mail delivery, meter reading, school bus routing etc. (Eiselt et al. 1995). Although there are many commercially available packages for arc routing, these packages cannot be used on the current problem, because it is a point-to-point routing problem.
TransCAD is the only software package that fully integrates GIS with demand modeling and logistics functionality (TransCAD 2006). It can be used to solve a variety of logistics problems such as vehicle routing/dispatching, arc routing, and network flow and distribution analysis. Satir (2003) did a case study for real-world P&D operations, using TransCAD to model and solve the problem. The results showed that TransCAD is a very effective scheduling tool for the VRP. However linehaul planning and scheduling problems cannot be solved by using this package.
The ILOG optimization packages are the most popular and considered the de facto optimization standard in OR. The main software components of these optimization packages are: ILOG CPLEX, ILOG Solver, ILOG Dispatcher, and ILOG Scheduler. ILOG (2003) discusses the various components in detail in their respective manuals. A brief description of each of these components from these manuals is summarized in this section.
ILOG CPLEX consists of C, C++, Java, and C# libraries that solve Linear Programming (LP) problems and its extensions such as network flow problems, quadratic programming (QP) problems, quadratically constrained problems, and Mixed Integer Programming (MIP) problems. In MIP problems, any or all of the LP or QP variables are further restricted to take integer values in the optimal solution.
ILOG Solver is a C++ library that allows the user to model optimization problems independently of the algorithms used to solve the problem. The two main techniques for solving the optimization problems are search strategies (Tabu Search or guided local search) and constraint propagation. A comparative study of eight constraint programming languages done by Fernandez and Hill (2003) showed the ILOG Solver to be the fastest, most efficient, and robust.
ILOG Dispatcher is a C++ library that offers features especially designed to solve problems in vehicle routing and maintenance-technician dispatching, This library is made up of classes that represent various aspects of routing plans, their vehicles, visits, and constraints. The Dispatcher finds various applications such as modeling a vehicle routing problem, solving a vehicle routing problem, modeling P & D operations, and routing multiple tours per vehicle. A solution to a routing problem involves the three stages of describing the problem, modeling the problem, and lastly solving the problem by using local search The Dispatcher can also be used to solve a VRP such as an assignment problem, or a P & D problem.
ILOG Scheduler is a C++ library intended to primarily help in solving scheduling and resource allocation problems. It works in conjunction with ILOG Solver and provides specialized modeling and algorithmic enhancements for scheduling problems. ILOG Scheduler makes it feasible to also take temporal and capacity constraints into consideration. The two types of temporal constraints that can be added are precedence constraints and time-bound constraints. While precedence constraints are used when the user needs to specify when an activity must start or end with respect to the start or end time of another activity, time-bound constraints are used to specify when an activity must start or end with respect to a given time.
ILOG CPLEX is not a practical choice for the problem at hand, because the problem requires a MIP formulation, which is extremely processor-intensive and time consuming for a problem of this size. ILOG Dispatcher could not be used for this problem either, because the Dispatcher is specifically designed for P & D type operations.
Using the ILOG Scheduler in conjunction with the ILOG Solver would have been the most appropriate choice to model and solve the problem. However, the problem at hand is not a pure scheduling problem, and has regulatory constraints and operational preferences in addition to the regular operational constraints. The pre-designed modeling environment would make the task of taking these additional regulatory constraints and operational preferences into account very cumbersome.
The latest product from ILOG, which is probably the most appropriate optimization package for linehaul planning is called Transport PowerOps, and was released as recently as April 2005. This package helps planners determine the lowest cost solutions for assigning vehicles, loading shipments and sequencing routes (ILOG PowerOps, 2006). The most important features of PowerOps are that it can handle hours of service regulations, driver rest rules, and multiple time windows. However, a shortcoming of this package is that the current problem requires different fleets to be subjected to different service regulations and for team and single driver vehicles to be handled differently. Some of the other disadvantages of using a package such as PowerOps (besides the company's potential dependency on an external package) are that the model and the operational requirements will have to be updated (building a new model) constantly to accommodate any changes or enhancements made to newer versions of the package, and this would make it difficult to integrate it with the existing IS. Operational preferences which cannot be taken into account by this package at present can be embedded using heuristics. However, this would require significant amount of work in addition to modeling the problem, which by itself is a tedious task. Although this package lacks some features and is not an off-the-shelf package (thus requiring specialized knowledge and expertise to make use of it), it is still a valuable asset to model and optimize linehaul operations.
There is a lack of software specifically designed for linehaul planning and scheduling.

Methods suitable for optimizing linehaul operations


A method for indicating status on a programmed communication device wherein each of one or more backlights is associated with a respective key of a plurality of keys. Status information to be communicated to a user of the communication device is then generated, and one or more backlights are illuminated according to a pattern corresponding to the status information. Thus, a visual graphical display is not necessary, cost is reduced, volume is conserved, and reliability is increased.

It is important that communication devices, such as cell phones, mobile telephone handsets, and the like, referred to herein as mobile telephones, be able to provide a user with relevant information about the operation of the mobile telephone, such as signal strength, remaining battery power, a dialed phone number, the phone number of an incoming call, and the like. Conventionally, such information has been provided via a visual graphical display, such as a liquid crystal display (LCD), light emitting diodes (LEDs), EL (electro-luminance).
There, however, are number of drawbacks associated with using such visual graphical displays. For example, visual graphical displays are costly, thereby potentially precluding many people from being able to own a mobile telephone. A continuing effort is also being made to make mobile telephones as volumetrically efficient as possible. It can readily be appreciated, however, that a visual graphical display will inherently limit the volumetric efficiency of a mobile telephone. To compensate for the additional volume required by a visual graphical display, the visual graphical display and/or keypad may be reduced in size, thereby rendering such display difficult to read, or such keypad difficult to use. Visual graphical displays also consume substantial battery power, a precious commodity for a mobile telephone. Still further, visual graphical displays are also prone to breakage, and a mobile telephone that relies on a visual graphical display is virtually worthless if its display is broken.
In an attempt to overcome the drawbacks associated with visual graphical displays, some mobile telephones are provided with dedicated indicators, which indicate the status of a single item, such as battery level or signal strength, without a visual graphical display. Such dedicated indicators, however, are generally limited to indicating only two states of an item, such as whether a battery level is below or above some predefined level. Furthermore, dedicated indicators also require volume, thereby imposing an additional limitation on how small a mobile telephone may be made.
Accordingly, a continuing search has been directed to the development of apparatuses and methods by which a mobile telephone may communicate information to a user in a manner which is relatively inexpensive, and which consumes less battery power and volume than conventional visual displays, and which is also less prone to breakage (i.e., more reliable) than conventional visual displays.

User interface and associated method for indicating status using keypad backlights


Elimination of truncation artifacts in Magnetic Resonance Images is accomplished by analaytically optimizing controllable parameters; i.e., filter characteristic and assymetry ratio when asymetrically sampling arid time domain filtering followed by complex conjugating the filtered data to reduce the Gibbs artifact.

Sharp transitions in the image cannot be well represented by time domain data which is sampled for a finite amount of time. Since real data must be truncated at some point in time, any discontinuity in the image will include an overshoot which is 9% of the magnitude of the discontinuity. This overshoot appears as "ringing" in the image. This ringing near sharp transitions is often referred to as the "Gibbs artifact" after Josiah W. Gibbs. Gibbs noted that with more coefficients the value of the overshoot in using the Fourier series does not diminish. However, the error (i.e., the overshoot) becomes confined to a region that shrinks around the discontinuity as the sampling time is increased. This causes the artifact to become less prominent.
Accordingly, the size of the sampling window used in obtaining the imaged data is increased, the amplitude of the overshoot remains the same, but the overshoot is compressed towards the edge of the discontinuity. However, taking more sampling points requires more time which reduces throughput. Also, as is well known, the signal-to-noise ratio (SNR) is proportional to the inverse of the square root of N where N is the number of sampling points used. Thus, taking more sampling points reduces the SNR while improving the spatial resolution.
In magnetic resonance image contrast resolution is often preferred over spatial resolution. Thus, reduced sampling in the phase encoding direction which reduces acquisition time should be preferred; especially since in the time saved the SNR could be improved by averaging several measurements. However, in the past the reduced sampling increased the ringing artifact cancelling any benefits of the improved SNR. Thus, until the invention U.S. Pat. No. 4,950,991, imaging experts have been reluctant to use low resolution images because of the increased Gibbs artifact.
The U.S. Pat. No. 4,950,991 uses a multiplicative filter in the time domain to reduce the amplitude of the overshoot and increase the SNR. The filter is used in conjunction with asymmetrical sampling and complex conjugation. The asymmetrical sampling and complex conjugation increases the spatial resolution based on a given number of actual sampling points. The filter reduces the spatial resolution of the image. However, the reduction in the spatial resolution of the filter is offset in the patent by the increase in spatial resolution afforded by the use of asymmetrical sampling and complex conjugation. Thus, the previously mentioned patent obtained a reduction in Gibbs artifact without adversely affecting the spatial resolution, the SNR or the scan time. It has now been found that the suppression of the ringing or truncation artifacts can be further improved and with no adverse effect on the resolution, the SNR or the scan time.
The improvement herein comprises the means and methods for optimizing the selection of system controllable parameters, i.e., the filter characteristics and the asymmetry of the sampling.

Reduction of truncation caused artifacts


A pseudo-random sequence generator characterized by comprising a plurality of substantially similar elements adapted to operate in parallel, each said element including: means for entering at least first and second different numbers into that element, and means for processing said numbers including multiplier means for creating intermediate numbers of higher value than either of said first and second numbers and modulating means for subsequently reducing those intermediate numbers to values below the higher of said first and second numbers, whereby said processing means is adapted to generate a first sequence that has a period of not less than half the number range of said first sequence; and means for combining the first sequences, number by number, from all the parallel elements to permit generation of a pseudo-random sequence of higher period.

Pseudo-random sequences of integers find many applications, for example in the sampling and simulation technologies. Sampling is an important factor for example in the pharmaceutical, biotechnological, medical and social sciences, and simulation of random events is used in many methods of destruction testing and prototype development in mechanical and civil engineering. Pseudo-random sequence generators also find applications in electronics, computer and communication technologies.
A random sequence is one in which, for all integral values of n, however large, the (n+1)th term in the sequence cannot be determined from knowledge of all the previous terms from the first to the (n)th. For example, data collected from 1,000,000 throws of a conventional six-faced die is of no assistance in determining the result of the 1,000,001th throw.
A pseudo-random sequence is a sequence for which it is perceived to be impossible to determine the (n+1)th term solely from knowledge of all the n previous terms unless n exceeds a very large number. In the state of the art, such a number is of the order of 1.times.10.sup.190 and there are statistical techniques available, such as the Berlekamp-Massey and the Sloane-Reeds tests which permit a formal judgement of the perception of impossibility. In this context the period of a sequence is the value of C such that, for all values of n, the (n+C) the term is identical to the (n)th term.
An object of the present invention is to make it possible to provide a pseudo-random generator wherein the period can be arranged to be very high while still retaining practical levels of speed and cost.


Provided is a moving picture processing method which prevents degradation of subjective image quality caused by a motion of a moving picture. The moving picture processing method includes the following steps: a motion compensation step (S116) of shifting a noise indicated by a stored noise signal (FMN) according to a motion of a moving picture indicated by an input image signal (VIN), by performing motion compensation on the stored noise signal (FMN) that is used for superimposition on a picture indicated by an input image signal (VIN) and is stored in a noise frame memory (102); and a superimposition step (S120) of superimposing the shifted noise, as a superimposition noise signal SN, onto a current picture to be processed which is indicated by an input image signal (VIN) and is a moving picture that appears after the motion has occurred.

A moving picture coding is known as a technology for coding a moving picture at a low bit rate and transmitting the coded moving picture, in a TV, a personal computer (PC), a cell phone or any other apparatus to display a moving picture.
With the moving picture coding technology as mentioned above, high frequency components included in a moving picture are removed when the moving picture is coded. Therefore, in the case where a moving picture presents meticulous patterns or the like, and coding and decoding are performed on that moving picture, the patterns may be lost in some cases.
A moving picture processing method for presenting noises as such meticulous patterns originally included in the moving picture by superimposing the removed high frequency components as noises on the decoded moving picture has been suggested (see Patent Reference 1).
According to the moving picture processing method of Patent Reference 1, an amount of noise to be added is determined using a parameter added to a bit stream representing a coded moving picture, and the noise is added as white noise to a decoded picture.
Thus, the moving picture processing method of Patent Reference 1 gives an impression to the viewers that the pictures are of high quality by superimposing noises.
Patent Reference 1: Japanese Laid-Open Patent Application No. 08-79765.


A tool for injecting solid fertilizer spikes into soil for tree and plant root nutrition utilizing elongated brackets to reduce the step-up height, form a fertilizer load chamber and to provide for a spring fertilizer spike retention mechanism such that the tool is fully operable in an upright position wherein a fertilizer spike is left embedded in the ground and detached from the tool without the need to remove the tool from the ground in a manner where, with one process of downward movement of the foot bar, two functions occur simultaneously, namely; the full injection of the fertilizer spike into the soil concurrent with the full release of the fertilizer spike from the tool by the complete ejection of the fertilizer spike from the fertilizer spike load chamber and the spring fertilizer spike retention mechanism. The tool is also provided with a spring wire that is adapted such that the fertilizer spike chamber, the injector tube and the foot bar are held in place in the load position until released by downward force by the operator on the top the foot bar.

The benefits of fertilizer spikes for providing nutrients for trees and shrubs directly below the ground surface is known. Prior fertilizer spike injection tools, however, remain: ineffectual, time consuming and/or cost prohibitive. The prior art shall be referenced to in detail, in this regard.
The available prior art relating to the field of invention might be divided into two tool groups—standalone tools that do not require other tools to used in conjunction with their operation by the user and tools that are auxiliary to other tools required in the operation by the user. For simplicity, it may serve to refer to the former as Primary prior art tools and the latter, as Secondary prior art tools. All prior art refereed to herein, except prior art, U.S. Pat. No. 3,892,552 issued to Jacob Douglas Gay, Jr., on Jul. 1, 1975, would be classified by this definition, as Primary prior art tools. The Primary prior art tools may be further grouped by the means in which the operator applies force onto the tool in the process of injecting the fertilizer spike into the soil, such as: 1) by hand, in a pushing fashion, 2) by hand, in a ramming fashion, 3) by a single foot, in a stomping fashion or 4) by two feet, in a jumping fashion. Product differentiation between each of these categories and within each of these categories is further apparent in that, within each of these categories, options exist based on whether, and if so by what means, will: the fertilizer spike be retained within the fertilizer spike load chamber, the fertilizer spike load chamber and/or fertilizer spike retention mechanism of the tool be inserted into the soil concurrent with the insertion of the fertilizer spike and the inserted fertilizer spike load chamber and/or fertilizer spike retention mechanism be removed from the soil while leaving the fertilizer spike behind.
Numerous problems of injection and ejection exist within each of these categories. Problems associated with the prior art where the fertilizer spike load chamber and/or fertilizer spike retention mechanism is injected into the soil concurrent with the injection of the fertilizer spike include: extraneous operator time, energy and effort required in the injection and ejection processes from overcoming the added friction from injecting extraneous mass such as the fertilizer spike load chamber and/or the fertilizer spike retention mechanism in conjunction with the fertilizer spike, from the soil adhering to the perimeter of the extraneous mass and from clogging and jamming of the fertilizer spike load chamber and/or the fertilizer spike retention mechanism with soil forced between the fertilizer spike and the walls of the fertilizer spike chamber and/or the fertilizer retention mechanism thereby failing to inject or eject the fertilizer spike, requiring maintenance prior to it's next use and causing a decreased range of soil firmness condition applications; difficult, complex, awkward or supplemental procedures and/or special expertise to inject the fertilizer spike into the soil; difficult, complex, awkward or supplemental procedures and/or special expertise and/or the requirement of auxiliary attachments to remove the tool from the soil after injecting the fertilizer spike while leaving the fertilizer spike behind; maintenance of the tool after removing the tool from the soil from soil adherence and exposure to corrosion form soil contamination.
Problems associated with the prior art category where there is excessive step-up height include: ineffectual operation, extraneous effort as well as awkward or unsafe operation from unstable and off-balance operation.
Problems associated with the prior art category where there is no fertilizer spike retention mechanism include: awkward/uncomfortable bending or kneeling to insert the fertilizer spike into the tool or into the ground.
Problems associated with the prior art category where there is no driver rod retention mechanism include: inadvertent displacement of the fertilizer spike prior to injection resulting in time-consuming as well as the need of bending or kneeling to insert the fertilizer spike into the tool resulting in awkward/uncomfortable/time-consuming operation.
Problems associated with the prior art category where there is hand/arm/shoulder movement to push the fertilizer spike into the soil include: extraneous operator time, energy and effort required in the injection process from a restriction to upper body strength resulting in deriving a limited amount of operator force and limiting the range of application due to soil firmness conditions.
Problems associated with the prior art category where there is hand/arm/shoulder movement to repeatedly ram the fertilizer spike into the soil include: excessive cost from damaged fertilizer spikes, extraneous operator time, energy and effort required in the injection process from clogging and jamming of the fertilizer spike load chamber, the fertilizer spike retention mechanism and/or the driver rod head with the end of a broken fertilizer spike, from ongoing replacement and maintenance of the striker pad and the rubber cushion, from partial absorption of the operator's force by the cushioned striker pad and from having to raise and lower a weighted striker rod thereby resulting in: failure to inject or eject the fertilizer spike, limited range of application due to soil firmness conditions and a diminished return of operator effort being derived.
Problems associated with the prior art category that is limited to single-foot pedal include: extraneous operator time, energy and effort required in the injection process from off-balance/off-center operation thereby resulting in deriving a limited amount of operator force and limiting the range of application due to soil firmness conditions as well as awkward or unsafe operation.
Problems associated with the prior art category that is limited to single-foot pedal with reciprocal movement include: extraneous operator time, energy and effort required in the injection process from off-balance/off-center operation thereby resulting in deriving a limited amount of operator force and limiting the range of application due to soil firmness conditions as well as awkward or unsafe operation in addition to extraneous operator energy from the binding resistance of off-centre pedal operation of the sliding foot pedal mechanism to the wall of the structure that contains it resulting in further reduction in the amount of operator force derived, further limiting of the range of application due to soil firmness conditions as well as increased awkward or unsafe operation.
Problems associated with the prior art category where the foot pedal is biased to a retracted position with a coil spring include: extraneous operator time, energy and effort is required during operation to counter the continual resistance of the coil spring resulting in a diminished return of operator effort being derived thereby limiting the range of application due to soil firmness conditions; time consuming, unstable/off-balance/operator jolting/unsafe operation from the disconnection of the driver head of the tool with the contact surface of the fertilizer spike at the time the fertilizer spike/pellet is inserted into this prior art to the moment of contact with the head of the driver rod and because of the step-ledge returning to the original step-on height should the operator step-off the tool before injection has been completed, as is most often the case, resulting in jolting of the operator, unstable and off-balance operation, loss of the visual depth of the injection obtained, a diminished return of operator effort being derived as well as possible clogging and jamming of the fertilizer spike load chamber, the fertilizer spike retention mechanism and/or the driver rod head with the end of a broken fertilizer spike from the ramming effect. There is also the added the cost of the coil spring itself as well.
Problems associated with the prior art where a plastic cap is used as an auxiliary tool in the injection process include: awkward/uncomfortable/timely bending or kneeling to insert the fertilizer spike into the ground; digging out the plastic cap prior art from the soil prior to it's next use; hitting one's fingers with a hammer while steadying the fertilizer spike; requiring other tools in the injection and ejection process which need to be maintained and which can be misplaced in the process.
Problems associated with the prior art without the inability to have simultaneous injection of the fertilizer spike into the soil with the ejection of the fertilizer spike from the fertilizer spike load chamber and the fertilizer spike retention mechanism include: extraneous operator time, energy and effort required in the injection and ejection processes.


A solid electrolytic capacitor includes a valve-acting metal substrate including a core part and a porous part disposed on at least one principal surface of the core part. A dielectric layer is formed in a surface of the porous part and a solid electrolyte layer is disposed on the dielectric layer. A conductive layer is disposed on the solid electrolyte layer and a sealing resin seals a principal surface of the capacitor element. A cathodic outer electrode is electrically connected to the conductive layer and an anodic outer electrode is electrically connected to the core part. An insulating layer is interposed between the core part and the sealing resin. The insulating layer, the sealing resin, and the anodic outer electrode are disposed on and above the core part in this order. A first anodic via electrode is formed in the sealing resin disposed on the insulating layer so as to penetrate the sealing resin. A second anodic via electrode is formed in the insulating layer disposed on the core part so as to penetrate the insulating layer. The core part is electrically drawn to a surface of the sealing resin through the first and second anodic via electrodes. The first anodic via electrode exposed at the surface of the sealing resin is connected to the anodic outer electrode.

Solid electrolytic capacitors typically include a capacitor element that includes a valve-acting metal substrate including a core part composed of a valve metal, such as aluminum, and a porous part formed in the surface of the core part, a dielectric layer formed in the surface of the porous part, a solid electrolyte layer disposed on the dielectric layer, and a conductive layer disposed on the solid electrolyte layer.
Japanese Unexamined Patent Application Publication No. 2008-135427 discloses a solid electrolyte capacitor wherein a plurality of capacitor elements are stacked on top of one another, the capacitor elements are then electrically connected to a lead frame, and resin sealing is subsequently performed by transfer molding or the like. In another case, the capacitor elements are electrically connected to a mount board, such as a printed circuit board, instead of a lead frame and resin sealing is subsequently performed.
The part of a solid electrolytic capacitor which is responsible for the formation of electrostatic capacity (hereinafter, such a part is referred to as "capacitance formation part") is the porous part, such as an etched layer, in which the dielectric layer is formed. In the production methods used in the related art, it is difficult to increase the ratio of the volume of the capacitance formation part to the overall volume of the capacitor. Thus, it has been difficult to produce a thin solid electrolytic capacitor.
The present invention was made in order to, inter alia, address the above issues. An object of the present invention is to provide a solid electrolytic capacitor that may have a small thickness.


The present invention relates to a gene being capable of modifying resistance against a heavy metal or salt, or accumulation properties, a recombination vector including the genes, and a transformant using the recombination vector. A gene having heavy metal resistance and accumulation properties includes a sequence encoding a transmembrane protein having five times repeated similar four transmembrane domains. A recombination vector includes the gene having heavy metal resistance and accumulation properties, and further includes a salt or drought resistance gene having at least one selected from the group consisting of a sequence encoding an ABC transporter including twice repeated six transmembrane domains and ATP-binding domains.

(a) Field of the Invention
The present invention relates to a gene being capable of modifying resistance against a heavy metal or salt, or accumulation properties, and a transformant produced using the gene. More particularly, the present invention relates to a gene being capable of modifying resistance against a heavy metal or salt, or accumulation properties, a recombination vector including the gene that improves resistance against salt or drought, a transformant produced using the recombination vector, a transgenic plant that has good resistance against a heavy metal, salt, or drought, efficiently removes or accumulates a heavy metal, and decreases uptake of a heavy metal, a phytoremediation method using the transgenic plants, and a method of developing a safety plant.
(b) Description of the Related Art
Heavy metals are major environmental toxicants, which cause reactive oxidation species generation, DNA damage, and enzyme inactivation by binding to active sites of enzymes in cells.
Contamination of the environment with heavy metals has increased drastically due to industrialization. By the early 1990s, the worldwide annual release had reached 22,000 tons of cadmium, 954,000 tons of copper, 796,000 tons of lead, and 1,372,000 tons of zinc (Alloway B J & Ayres D C 1993 Principles of environmental pollution. Chapman and Hall, London). The soils contaminated with heavy metal inhibit normal plant growth and cause contamination of foodstuffs. Many heavy metals are very toxic to human health and carcinogenic at low concentrations.
Therefore removal of heavy metals from the environment is an urgent issue. Traditional methods of dealing with soil contaminants include physical and chemical approaches, such as the removal and burial of the contaminated soil, isolation of the contaminated area, fixation (chemical processing of the soil to immobilize the metals), and leaching using an acid or alkali solution (Salt D E, Blaylock M, Kumar N P B A, Viatcheslav D, Ensley B D, et al. 1995. Phytoremediation: a novel strategy for the removal of toxic metals from the environment using plants. Bio-Technology 13, 468-74; Raskin I, Smith R D, Salt D E. 1997 Phytoremediation of metals: using plants to remove pollutants from the environment. Curr. Opin. Biotechnol. 8, 221-6). These methods, however, are costly and energy-intensive processes.
Phytoremediation has recently been proposed as a low-cost, environment-friendly way to remove heavy metals from contaminated soils, and is a relatively new technology for cleanup of contaminated soil that uses general plants, specially bred plants, or transgenic plants to accumulate, remove, or detoxify environmental contaminants. The phytoremediation technology is divided into phytoextraction, rhizofiltration, and phytostabilization. Phytoextraction is a method using metal-accumulating plants to extract metals from soil into the harvestable parts of the plants; rhizofiltration is a method using plant roots to remove contaminants from polluted aqueous streams; and phytostabilization is the stabilization of contaminants such as toxic metals in soils to prevent their entry into ground water, also with plants (Salt et al., Biotechnology 13(5): 468-474, 1995).
Examples of phytoremediation are methods using the plants of Larrea tridentate species that are particularly directed at the decontamination of soils containing copper, nickel, and cadmium (U.S. Pat. No. 5,927,005), and a method using Brassicaceae family (Baker et al., New Phytol. 127:61-68, 1994).
In addition, phytoremediation using transgenic plants that are generated by introducing genes having resistant activity for heavy metals have been attempted. Examples of heavy metal resistant genes are AtATM3 (ABC transporters of mitochondria), CAX2 (Calcium exchanger 2), cytochromium P450 2E1, NtCBP4 (Nicotiana tabacum calmodulin-binding protein), GSHII (glutathione synthetase), AtPcr1 (plant cadmium resistance), AtPDR12 (pleiotropic drug resistance), or MRT polya peptide (metal-regulated transporter polypeptide). AtATM3 is an ABC-type transporter that improve cadmium and lead resistance of over-expressed transgenic plants, and increases cadmium contents in transgenic plants (Kim et al., Plant Physiol. 140:922-932, 2006), CAX2 accumulates heavy metals including cadmium and manganese in plants (Hirschi K D et al., Plant Physiol. 124:125-134, 2000), cytochromium P450 2E1 uptakes and decomposes organic materials such as trichloroethylene (TCE) (Doty S L et al., Proc. Natl. Acad. Sci. USA 97:6287-6291, 2000). Transgenic plant transformed with NtCBP4 has resistant activity for nickel (Arazi T et al. Plant J. 20:171-182, 1999), GSHII accumulates cadmium (Liang Zhu Y et al., Plant Physiol. 119:73-80, 1999), plants that over-express AtPcr1 has cadmium resistance by decreasing cadmium content (Song et al., Plant Physiol. 135:1027-1039, 2004, Korean Patent Application No. 2003-0058299 and U.S. patent application Ser. No. 10/907,694), transgenic plants transformed with AtPDR12 improves lead resistance by lead contents in a plant (Lee et al., Plant Physiol. 138:827-836, 2005), and MRT polypeptides remove heavy metals such as iron, cadmium, manganese, and zinc from soils (U.S. Pat. No. 5,846,821.
Recently, it is reported that bacteria and yeast genes as well as plant genes can be introduced into a plant to effectively improve heavy metal resistance and accumulation. For example, merB (organomercurial lyase) was reported to be able to decompose organic mercury materials (Bizily S P et al., Proc. Natl. Acad. Sci. USA 96:6808-6813, 1999). In addition, a ZntA gene, which is a P-type pump of bacteria, was reported to increase resistance against and also, less uptake them when it was over-expressed by merB (Lee et al., Plant Physiol. 133:589-596, 2003; Korean Patent No. 0515520). An Ycf1 (yeast cadmium factor1) gene, which is an ABC-type carrier of yeast, was reported to be expressed in a plant and thereby, increase resistance against cadmium and lead and accumulation thereof when it was over-expressed by merB (Song et al., Nat Biotechnol. 21:914-919, 2003; International patent PCT/KR02/01934). Likewise, another method was reported that a transgenic plant could be developed by expressing a MRP-type ABC carrier of yeast in a plant when it was over-expressed by merB (Korean Patent No. 0480843).
However, these transgenic plants including a gene with heavy metal resistances outgrew a wild-type one in a contaminated soil but did not have much improved accumulation in the shoot region. In general, a plant for environment purification should not only have resistances against contamination materials but also be able to carry them to the shoot region and thereby, accumulate them there. The reason is that the shoot region of a plant can be more safely and economically harvested and disposed rather than the root.
However, a conventional transgenic plant including a gene with heavy metal resistance a little outgrew a wild-type one in a contaminated soil but turned out to be not be able to effectively pump up heavy metals from root to shoot region and thereby, accumulate them in the shoot region.
In general, a plant uptakes various contamination materials in the environment when it uptakes water. Accordingly, when a plant can uptake more water and transpire it, it can accumulate more contamination materials in its body faster. Therefore, this kind of a plant can decrease contamination in the environment in a shorter term than a wild-type one, contributing to diminishing time and cost for purifying the environment.
In addition, water insufficiency is world-widely raised as a serious problem. The world already started to be desertificated in several areas. This is subsequently causing another serious problem in farming and environment. Therefore, a plant that can need less water and successfully survive in a dry and highly-salted environment should be desperately developed. In particular, when a plant is developed for economically purifying environment in a dry area, it should ideally have improved resistance against drought as well as contamination materials. On the other hand, when a plant can decrease transpiration, it can contribute to purifying environment and increasing agricultural productivity in a very arid area.
Unlike a plant for purifying environment, a crop is required to uptake contamination materials to a minimum. If a crop absorbs heavy metals or other contamination materials, it can hurt people and domestic animals consuming it. Therefore, a crop cannot be poisoned but safe from heavy metals by expressing a gene removing a heavy metal therein. In addition, when a gene accumulating a heavy metal in a cell is artificially less expressed or suppressed to oppositely work, a transgenic plant including the gene can have less accumulated heavy metals than a wild-type one, contributing to development of a safer plant.
On the other hand, a gene related to have heavy metal resistance, salt resistance, drought resistance, and the like can be used to rehabilitate an environment. The rehabilitation of environment can be accomplished by recovering nature artificially or naturally destroyed once and rebuilding ecosystem as it used to be. Accordingly, the environment can not only be refreshed but natural resources also can be preserved, so that human can cohabit with other living species. A method of rehabilitating environment includes removal of contamination materials, planting of a resistant plant, reintroduction of extinct animals, and the like. For example, Daegoo arboretum was created by planting a wild plant and a medicinal plant in a landfill used for dumping trash and thereby, changing it into an ecosystem education center and a rest place. In addition, Kwangjoo Ooncheon reservoir used to be contaminated due to domestic sewage but was now rehabilitated into a natural ecosystem park. However, a landfill may release cadmium with leachate. An abandoned mine can be severely arid. Therefore, genes with high resistance against heavy metals and drought can be usefully used for rehabilitating a landfill or an abandoned mine. In addition, a gene with high salt resistance can be used for rehabilitating a reclaimed land with a high salt concentration.

Genes that alter capacity to accumulate heavy metals and salts or resistance to heavy metals, salts or drought, and transformants expressing the genes


The present invention is directed to providing, in a plurality of information processing apparatuses which transmits and receives objects, a technique for causing the display contents in the apparatuses to be related by the apparatuses performing simple exchange of information. An information processing apparatus includes a display control unit configured to cause, based on the information on the azimuth direction in which an object displayed on a screen has been moved, from other apparatus that transmits the information and the information indicating the azimuth direction in which the screen of the information processing apparatus has been directed, an object which is the same as an object displayed on a screen of the other apparatus to appear from an azimuth direction opposite of the azimuth direction in which the object displayed on the screen of the other apparatus has been moved, in the screen of the information processing apparatus.

1. Field of the Invention
The present invention relates to a technique for causing display contents of a plurality of information processing apparatuses to be related.
2. Description of the Related Art
There is a technique for causing a plurality of display devices to cooperate and be virtually used as one large display device. For example, if the plurality of display devices is to be used as one display device in a personal computer (PC), an arrangement of the display devices is preset on the PC. Display output to each of the display devices is controlled according to the information on the set arrangement.
Further, in recent years, information processing apparatuses such as a tablet PC have become widely-used. "Multi-Smartphone-Display Applications that React Dynamically to Display's Layout, Information Processing Society of Japan Interaction 2012" discusses the following technique. The technique assumes that screens in two information processing apparatuses are screens in the same space, and relates the contents of displayed images. More specifically, a pinch operation bridging over two screens is input to the two information processing apparatuses. As a result, a relation between positions in which the information processing apparatuses are arranged is set, so that the display images in the respective apparatuses are related.
However, according to the technique discussed in "Multi-Smartphone-Display Applications that React Dynamically to Display's Layout, Information Processing Society of Japan Interaction 2012", it becomes necessary to input the pinch operation over the two screens every time an orientation of at least one of the information processing apparatuses changes.

Information processing apparatus which cooperates with other apparatus, and information processing system in which a plurality of information processing apparatuses cooperates


Disclosed is an aqueous binder composition for mineral fibers that comprises a water-soluble binder component produced by reacting, in one or more steps, at least one alkanolamine, at least one carboxylic anhydride and at least one polyalkylene glycol component selected from polyalkylene glycols, copolymers and derivates thereof and, optionally, treating the reaction product with a base.

Mineral fibre products generally comprise man-made vitreous fibres (MMVF) such as, e.g., glass fibres, ceramic fibres, basalt fibres, slag wool, mineral wool and stone wool, which are bonded together by a cured thermoset polymeric binder material. For use as thermal or acoustical insulation products, bonded mineral fibre mats are generally produced by converting a melt made of suitable raw materials to fibres in conventional manner, for instance by a spinning cup process or by a cascade rotor process. The fibres are blown into a forming chamber and, while airborne and while still hot, are sprayed with a binder solution and randomly deposited as a mat or web onto a travelling conveyor. The fibre mat is then transferred to a curing oven where heated air is blown through the mat to cure the binder and rigidly bond the mineral fibres together.
In the past, the binder resins of choice have been phenol/formaldehyde resins which can be economically produced and can be extended with urea prior to use as a binder. However, the desire to minimize Volatile Organic Compound (VOC) emissions from products in conjunction with existing and proposed legislation directed to the lowering or elimination of formaldehyde have led to the development of formaldehyde-free binders such as, for instance, the binder compositions based on polycarboxy polymers and polyols, as disclosed in EP-A-583086, EP-A-990727 and U.S. Pat. No. 5,318,990.
Another group of non-phenol/formaldehyde binders for mineral fibres are the addition/elimination reaction products of aliphatic and/or aromatic anhyrides with alkanolamines, e.g., as disclosed in WO 99/36368, WO 01/05725, WO 01/96460, WO 02/06178, WO 2004/007615 and WO 2006/061249. These mineral fibre binders are water soluble and exhibit excellent binding properties in terms of curing speed and curing density. However, despite these disclosures, there is a continuing need for identifying new formaldehyde-free, curable aqueous compositions suitable for use as a binder for mineral fibre products.
A type of product suffering from similar environmental problems associated with conventional phenol/formaldehyde binders are growth substrates for plants which are based upon man-made vitreous fibres or other porous substrates; see, for instance, GB-A-1336426. These substrates may, e.g., be provided in the form of slabs, blocks, plugs or other coherent products or in the form of granulate.
Conventional plant growth products generally comprise a binder, often a phenol-formaldehyde resin or urea-formaldehyde resin, which provides integrity to the product. After application of the binder, the products are subjected to curing at high temperatures in a curing oven.
It is essential that these plant growth substrates are able to take up and hold water, and therefore a certain wettability is required. Phenol-formaldehyde resins, and to lesser degree urea-formaldehyde resins are, however, found to impart water repellency to mineral wool products and, therefore, it is well-known to include a wetting agent in the plant growth substrate in order to achieve the desired hydrophilicity and wettability; see, for instance, WO 92/04824 and WO 01/82683. Such wetting agents must exhibit good environmental compatibility, in particular, low phytotoxicity. Moreover, in view of the working conditions employed during production of the plant growth substrates, they must have good thermal stability and also provide products having proper wet and dry compression strength in addition to the desired water-uptake capacity and water retaining capacity.
However, over time conventional wetting agents often are washed out of the plant growth substrate leaving a product of insufficient wettability and water retaining capacity.

Aqueous binder composition for mineral fibers


The invention is directed to a broadband, low-profile antenna structure that in one embodiment includes a compound radiator and a ground plane. The compound radiator is comprised of a dipole radiator portion and a Vivaldi radiator portion that is electrically connected to the dipole radiator portion. In operation, the dipole radiator portion operates in the lower end of the bandwidth and the Vivaldi radiator portion operates in the upper end of the bandwidth.

There is a need for a broadband or broad bandwidth, low-profile antenna. The bandwidth of an antenna is typically defined as the difference between the low frequency (flow) and high frequency (fhigh) at which the power output of the antenna is within 3 dB of the maximum power output of the antenna. In a broadband or broad bandwidth antenna, the ratio of fhigh to flow is greater than 3:1. The profile of an antenna that includes a ground plane and one or more radiators that are all located to one side of the ground plane refers to a plot of the shortest distance between each point associated with the radiators and the ground plane. For a broadband antenna to be considered to be low-profile, the maximum distance in the profile must be less than λ/2 at flow.
An example of a broadband, high-profile antenna can be found in currently known synthetic-aperture radars. The antenna in such a radar is a single-beam antenna that is capable of broadband performance, mounted to a moving platform (e.g., an aircraft), and used to obtain high spatial resolution images of a target region. To elaborate, the antenna is used to transmit pulses of radio signals of varying wavelengths within the bandwidth and receive echo waveforms that are coherently detected and subsequently processed to obtain a high spatial resolution image of the target region. Currently, the known single-beam, broadband antennas that are used in such radar systems have a high profile (i.e., greater than λ/2 at flow) that is disadvantageous. For example, a high profile limits the application of the antenna to moving platforms that have the space to accommodate the profile of the antenna. A high profile can also adversely affect the operation of the moving platform with which antenna is associated. For example, if the antenna is associated with an aircraft, the high profile may require that a significant portion of the antenna project beyond the normal "skin" of the aircraft and to an extent that adversely affects the aerodynamics of the aircraft.

Broadband, low-profile antenna structure


In the manufacture of integrated labels it is desirable to apply pressure sensitive adhesive in a continuous manner, yet it is undesirable for active adhesive to be on one or more edges of the form since active adhesive can interfere with nip rollers upon entering a laser or other non-impact printer, or can otherwise interfere with proper operation of the printer. By using an adhesive--that is de-tackified by direct exposure to a sufficient type and dosage of electromagnetic radiation (such as a hot melt adhesive de-tackified by applying about 3000 mJ/cm.sup.2 total dosage of ultraviolet radiation)--that problem may be avoided. Apparatus for producing integrated labels with the adhesive at one or more edges being de-tackified may include a first conveyor for conveying sheets (either in stacked or single sheet form) in a first direction, and at least one ultraviolet radiation source mounted adjacent a side of the conveyor parallel to the first direction. A stacker, packaging device (such as a shrink wrap machine), 90.degree. conveyor, and/or turn table may also be utilized.

Business forms in cut sheet format having at least one label (with pressure sensitive adhesive) and suitable for variable printing in a non-impact printer (such as a laser printer or other printer using a heat-curable toner) are referred to as integrated labels, and are exemplified by U.S. Pat. No. 5,129,682. In current manufacturing processes a hot melt extrusion die adhesive application method is utilized in which a continuous stream of pressure sensitive hot melt adhesive is applied to a release web, the release web is laminated to a paper web, one or more labels are die cut, and a continuous form format is cut into individual sheets. The paper face sheet typically comprises 20-28 lb. per 500 sheets of paper per ream with dimensions of 17.times.22 inches! bond paper, while the release sheet is typically 25-50 lb. per 500 sheets of paper per ream with dimensions of 22.times.36 inches! weight material. While this technique is extremely efficient and cost effective, the integrated label produced has pressure sensitive adhesive extending to at least one, and typically to two opposite cut edges of each form. This presents a significant contamination problem in non-impact printers for variably printing indicia on the integrated labels, such as laser printers or other non-impact printers utilizing a heat curable toner to apply indicia. Contamination can occur in the nip rolls for the laser printer, or in other printer paper guiding and feed system components, and the build up of adhesive can eventually cause poor performance of the printer or terminate its operation altogether, the adhesive building up due to the tacky nature thereof.
One way in which the above mentioned problem can be avoided is to apply the adhesive in a pattern rather than in a continuous strip. When applied in a pattern, the pattern includes a hiatus at the edges where the continuous web will be cut into sheets. However this manufacturing method is slower and more costly than the extrusion die continuous strip method. Therefore it is desirable to be able to solve the problem of the adhesive contaminating laser printers which act upon the integrated labels while at the same time allowing manufacture using the continuous strip application of pressure sensitive adhesive.
According to the present invention the desired results of preventing printer contamination as a result of adhesive built up, while still allowing production of the integrated labels utilizing the continuous strip method, are provided. The invention accomplishes these desired goals by utilizing as the pressure sensitive adhesive an adhesive that becomes de-tackified by direct exposure to a sufficient type and dosage of electromagnetic radiation. Typically this is accomplished utilizing a specially formulated hot melt adhesive that is sensitive to ultraviolet energy so that when exposed to, e.g., about 3000 mj/cm.sup.2 total dosage of ultraviolet radiation, the edges of the integrated labels (where the release and bond sheet overlap) is rendered de-tackified, and therefore will not interfere with operation of, or otherwise contaminate, a non-impact printer. There are several aspects of the present invention employing this basic concept.
According to one aspect of the present invention a method of producing a sheet having at least one label and suitable for variable printing in a nonimpact printer, is provided. The method comprises the steps of: (a) Applying a continuous strip of pressure sensitive adhesive, that is de-tackified by direct exposure to a sufficient type and dosage of electromagnetic radiation, to a release sheet. (b) Applying the release sheet to a first face of a web of paper so that the release sheet covers only a portion of the first face and the adhesive is attached to the web. (c) Forming at least one label in each of a plurality of predetermined lengths of the web at the portion of each web predetermined length covered by the release sheet. (d) Cutting the web into individual sheet lengths, each sheet having at least a first edge of the paper at which the release sheet is provided. (e) Exposing the first edge to the sufficient type and dosage of the electromagnetic radiation that de-tackifies the adhesive so that the adhesive at the first edge becomes de-tackified. And, (f) subsequently using the sheet in a heat-curable toner non-impact printer.
The adhesive is preferably rendered de-tackified by ultraviolet radiation, and step (e) is practiced by exposing a sheet to ultraviolet radiation, e.g. exposing hot melt adhesive to about 3000 mj/cm.sup.2 total dosage of ultraviolet radiation.
The first edge may be a common edge of the paper and release sheet, and there may be the further step (g), between steps (d) and (e) of stacking a plurality of sheets in a stack with substantially aligned first edges. Step (e) is then practiced with the sheets in the stack (although alternatively step (e) may be practiced on individual sheets). Step (g) may be further practiced by placing chip board material on the top and the bottom of the stack.
Steps (a) through (d) may be practiced so that opposite first and second edges are commonly formed by the paper and release sheet, and step (e) may be practiced to apply electromagnetic radiation to the first and second edges one immediately after the other. Steps (a) through (d) may also be practiced so that a third edge, perpendicular to and extending between the first and second edges, is also commonly formed by the paper and release sheet, in which case there is the further step--either before or after step (e)--of exposing the third edge to a sufficient type and dosage of the electromagnetic radiation that the adhesive at the third edge becomes de-tackified.
There may also be the further steps, prior to step (f) of stacking a plurality of sheets in a stack, wrapping the stack in packaging, transporting the packaging to the site of the non-impact printer, and unpackaging the stack at the site of the non-impact printer.
According to another aspect of the present invention there is provided a method of acting upon a sheet comprising a first ply of paper and a second ply of a pressure sensitive adhesive release material overlapped with the first ply, with a pressure sensitive adhesive in a continuous strip between the first and second plies and holding them together in overlapped position, the second ply adjacent the first ply at at least a first edge of the first ply, the pressure sensitive adhesive being capable of being rendered de-tackified when directly exposed to a sufficient type and dosage of electromagnetic radiation, and at least one label formed by the first ply where the first and second plies overlap, the method comprising the step of (a) applying to the first edge the type of electromagnetic radiation with sufficient intensity and duration so that it de-tackifies the adhesive, so that the adhesive at the first edge becomes de-tackified. The detailed operations and steps, as described above, may also be utilized in the practice of this aspect of the invention.
The invention also comprises an integrated label. The integrated label of the invention has the following components: A first paper ply having a quadrate configuration and four edges and a first area. A second quadrate ply comprising a pressure sensitive adhesive release sheet having four edges. The first and second plies overlapping, including a first edge of the first ply aligned with or overlapped by the second ply. A continuous strip of pressure sensitive adhesive disposed between the overlapping portions of the first and second plies, releasably holding them together. At least one label formed in the first ply at the overlapping portions of the first and second plies. And, the adhesive at the first edge being de-tackified so that it will not stick to or interfere with continued operation of component parts of a heat-curable toner non-impact printer if the integrated label is passed through the printer, and the adhesive is tacky at the at least one label.
The second ply may have a second area significantly smaller than the first area, and the first edge of the first ply may be aligned with the first edge of the second ply and a second edge of the first ply aligned with a second edge of the second ply. In this case the adhesive at the second edge is also de-tackified so that it will not stick to component parts of or interfere with continued operation of a heat-curable toner non-impact printer if the integrated label is passed through the printer. The integrated label may be in a stack with a plurality of identical integrated labels having aligned edges, and the pressure sensitive adhesive may be a hot melt adhesive that becomes de-tackified when exposed to ultraviolet radiation.
According to another aspect of the invention there is provided apparatus for handling multi-ply sheets with pressure sensitive adhesive between the plies which is rendered de-tackified by direct exposure to ultraviolet radiation. The apparatus comprises: A stacker for stacking a plurality of sheets into a stack having aligned edges, and at least one ultraviolet radiation source emitting ultraviolet radiation that renders the adhesive de-tackified. A first conveyor may also be operatively associated with the stacker for conveying sheets in a first direction, and having first and second sides generally parallel to the first direction. The at least one ultraviolet radiation source preferably is adjacent to one of the first and second sides of the first conveyor for emitting ultraviolet radiation so that it is directed upon at least one edge of the sheets in the stack when the stack is on the first conveyor.
Each source of ultraviolet radiation may be a 300 nanometer nominal frequency, 300 watt/inch ultraviolet radiation source. The at least one source may comprise first and second sources mounted adjacent to the first and second sides of the first conveyor, respectively, and the first source may be mounted for movement toward and away from the second source to readily accommodate different size sheet edges between them. A third ultraviolet radiation source associated with a second conveyor extending perpendicular to the first conveyor also may be provided. Packaging means, a 90.degree. conveyor, a turn table, and like components may also be associated with the apparatus, and a stacker may be provided either upstream or downstream of the first conveyor in the first direction.
It is the primary object of the present invention to provide for the quick and inexpensive extrusion die continuous strip method production of integrated labels, which labels do not have active adhesive at the edge portions thereof so that they will not interfere with continued operation of non-impact printers. This and other objects of the invention will become clear from an inspection of the detailed description of the invention, and from the appended claims.

De-tackified continuous extrusion process applied integrated label product


A method and an apparatus for pulling a single crystal are disclosed. A neck portion, a corrugated portion, and a single crystal are formed below a seed crystal held by a seed chuck. When the corrugated portion is raised to a predetermined position (where lifting jig can hold the corrugated portion) by the seed chuck, the rising speed Va of the seed chuck is reduced, and a slider that supports a seed chuck lifting mechanism is raised at a speed Vb in order to maintain a constant pulling speed of the single crystal. Eventually, the pulling by the seed chuck is switched to the pulling by the slider. Subsequently, the lifting jig provided on the slider is raised slightly by a moving mechanism so that the crystal holding portions of the lifting jig are brought into contact with the corrugated portion and 1-50% of the weight of the crystal is shifted to the lifting jig. This enables safe and accurate growth of a heavy single crystal in accordance with, for example, the CZ method.

1. Field of the Invention
The present invention relates to a crystal pulling method and apparatus employing, for example, the Czochralski method (the CZ method), and particularly to an improvement on a technique for mechanically holding a heavy single-crystal in order to pull the crystal safely and reliably, which improvement reduces variations in the diameter of a growing crystal at a point of time when the crystal is held, thereby enabling accurate growth of the crystal.
2. Description of the Related Art
Regarding a method of pulling a single crystal from a melt of a semiconductor material, such as silicon, contained in a crucible, the present applicant have proposed an improved pulling technique as described in, for example, Japanese Patent Application No. 8-212055.
Conventionally, a single crystal is pulled in a manner as shown in FIG. 5: a seed crystal 53 held by a seed chuck 52 at the lower end of a wire 51 is brought into contact with material melt contained in an unillustrated crucible, and the seed crystal 53 is pulled by a seed chuck lifting mechanism 54 in order to grow a single crystal C below the seed crystal 53. In order to improve this conventional manufacturing method, the technique disclosed in Japanese Patent Application No. 8-212055 employs an apparatus having the following structure: a retaining case 57 is mounted on a slider 56 which is vertically moved by an unillustrated slider moving mechanism; the seed chuck lifting mechanism 54 for winding the wire 51 is provided within the retaining case 57; and a lifting jig 60 composed of paired members is provided below the retaining case 57. The lower ends of the paired members of the lifting jig 60 are opened and closed through operation of cylinder units 58. At the beginning of pulling, the single crystal C is pulled by the seed chuck 52, and pulling by the seed chuck 52 is switched to pulling by the lifting jig 60 when the crystal C has grown to become heavy.
That is, initially, with the slider 56 fixed at a certain position, the seed crystal 53 held by the seed chuck 52 is brought into contact with the material melt, and subsequently the seed chuck 52 is pulled by the seed chuck lifting mechanism 54. As a result, as shown in FIG. 5A, a neck portion 59, a corrugated portion Ck, and the single crystal C are formed below the seed crystal 53.
When the corrugated portion Ck rises to a predetermined position shown in FIG. 5B, the lifting jig 60 is operated as shown in FIG. 5C such that the lower end portions of the paired members of the lifting jig 60 approach the smaller-diameter portion of the corrugated portion Ck with a clearance remaining between the lower end portions of the paired members of the lifting jig 60 and the smaller-diameter portion of the corrugated portion Ck. Subsequently, as shown in FIG. 5D, the slider 56 is raised, while the seed chuck lifting mechanism 54 is operated in reverse in order to lower the single crystal C relative to the slider 56, such that the larger-diameter portion of the corrugated portion Ck comes into contact with and sits on the lifting jig 60.
At this time, control is performed such that the sum of the rising speed Vb of the slider 56 and the rising speed Va of the seed chuck 52 relative to the slider 56 becomes identical to the previous rising speed of the seed chuck 52 as measured when solely the seed chuck 52 was engaged in pulling. Also, when a predetermined portion of the entire load of the single crystal C has shifted to the lifting jig 60, the seed chuck lifting mechanism 54 is stopped, as shown in FIG. 5E, so that the pulling operation is performed by only the lifting jig 60; i.e., only the slider 56 is raised.
Since the lifting jig 60 contacts the corrugated portion Ck of the crystal not in a lateral direction but in the vertical direction, the crystal can be pulled safely and reliably without generation of dislocation in the crystal.
In this technique, when the pulling by the seed chuck 52 is switched to the pulling by the lifting jig 60, as shown in FIG. 6, the rising speed Va of the seed chuck 52 is decreased, and eventually the seed chuck 52 is lowered relative to the slider 56 (lifting jig 60) (Va becomes negative) in order to shift the weight of the single crystal C to the lifting jig 60.
In the above-described technique, the weight of the single crystal C acting on the seed chuck 52 is shifted to the lifting jig 60 while the speed Vb of the lifting jig 60 and the speed Va of the seed chuck 52 are changed in order to switch the pulling means. Therefore, when the lifting jig 60 deforms due to the weight of the crystal or slip occurs between the lifting jig 60 and the corrugated portion Ck, the speeds Va and Vb must be controlled in consideration of an increased number of factors including the above-described deformation and slip, so that the speed control becomes complex and fine adjustment becomes difficult to perform.
If fine adjustment of the speeds Va and Vb cannot be performed correctly, the growth rate of the single crystal varies, so that variations in the diameter of the crystal and other problems occur.
Therefore, there has been strong demand for a technique that can accurately control the diameter of a single crystal being pulled through simplified growth rate control, without use of the above-described complicated control.


An apparatus for washing parts includes a cleaning chamber including a spray portion and a reservoir portion. The spray portion includes a support for the parts and a spray bar having at least one orifice for distributing a cleaning solution. The reservoir portion stores and collects the cleaning fluid. A thermal energy source adjusts and maintains the operating temperature of the cleaning solution in the reservoir portion. The thermal energy source retains a transfer fluid and includes a heater for adjusting a temperature of the transfer fluid. A conduit extends through the thermal energy source and defines a passageway for the cleaning fluid. A pump draws the cleaning fluid through the passageway and discharges the cleaning solution through the spray bar, such that the operating temperature of the cleaning solution is increased.

A parts washer is an apparatus that cleans various parts including, but not limited to machinery and machine parts. Current parts washers generally use an aqueous cleaning solution to remove such things as grease, carbon, resins, tar, inks and other grime from dirty parts like engine parts, tools, etc. Parts washers have also been known to use hydrocarbon solvent cleaning solutions to clean parts.
A conventional automatic aqueous parts washer includes a housing with a door to access a cleaning chamber having tray disposed therein for supporting parts. A pump pulls a cleaning solution from a reservoir and delivers the cleaning solution under pressure to a series of nozzles directed toward the parts disposed on the tray. A heater disposed in the reservoir is also commonly used for increasing the temperature of the aqueous cleaning solution, when desirable.
A major disadvantage of conventional part washers is the inability of the heater to maintain the temperature of the aqueous cleaning solution in an effective range, i.e. 120° F. to 160° F. Aqueous cleaning solutions must be stabilized in the effective range during a cleaning cycle in order to properly clean parts. Conventional parts washers attempt to maintain the cleaning solution in the effective range by using a heater configured for the cleaning solution capacity and workload of the machine. Such conventional heating elements are usually immersion heaters in direct contact with the aqueous cleaning solution and when new, easily raise the temperature of the cleaning solution into the effective range. However, once parts washing has commenced, the cleaning solution temperature drops rapidly, usually in less than 5 minutes. The heating element at maximum rated output cannot maintain the temperature of the cleaning solution above 120° F., for any extended period of time which is required to clean parts effectively. The cleaning solution cools as a result of ambient losses to the surrounding environment, atomization of the cleaning solution as it exits the nozzles and heat energy dissipated into the parts to be cleaned to bring them up to solution temperature.
Another disadvantage, and basis for the above disadvantage, is that a significant majority of the conventional aqueous parts washers are sold and used in a commercial setting, such as a car dealership repair shop, or a residential setting. Standard 120 volt/single phase electrical circuits in commercial and residential settings are often limited to 15 amps. In rare instances a 20 amp circuit may be available. Usually, custom installation or retrofit of an 120 volt electrical circuit with power handling capability of more than 15 amps is necessary. This results in increased costs to the facility owner. Alternatively, 240 or 480 volts of single or multi-phase circuits may be installed, all at significant cost to the owner/operator. Moreover, parts washers designed to operate on increased capacity electrical circuits also cost more to manufacture. Accordingly, conventional parts washers cannot be modified to use additional heaters because the power capacity of the electrical circuits is limited.
Another disadvantage of prior art parts washers is that the immersion heater is in direct contact with the aqueous cleaning solution. During the parts washing process, sludge, scale and other particulates, which are common in aqueous cleaning solutions, accumulate and are baked on the heater elements resulting in buildup of scale deposits on the heater. The scale deposits then act as an insulator. As a result, over time, heat transfer to the cleaning solution becomes less efficient, energy/operating costs are increased, life expectancy of the heater elements is shorter and periodic maintenance is increased.
Therefore, there is a need in the art for an improved parts washing apparatus having a novel structure and function for adjusting, increasing and maintaining the temperature of an aqueous cleaning solution that is operational on a standard 120 volt/15 amp electrical circuit, requires substantially reduced maintenance and less operating energy, cleans longer and more batches of parts compared to conventional parts washers, and overcomes the aforementioned disadvantages of prior art parts washers.


A method and system for analysis of data, including creating a first node, determining a first hyper-cube for the first node, determining whether a sample resides within the first hyper-cube. If the sample does not reside within the first hyper-cube, the method includes determining whether the sample resides within a first hyper-sphere, wherein the first hyper-sphere has a radius equal to a diagonal of the first hyper-cube.

Artificial neural networks may be used to analyze operation in a system based on known values of the system. For example, a user may be interested in analyzing sensor data, such as sensor data from semi-conductor processing equipment. A Radial Basis Function (RBF) network is an artificial neural network that uses radial basis functions as activation functions. In a typical RBF network, an RBF node or neuron is responsible for determining the activation value of the node, where each node has multiple inputs and one output. RBF networks typically can only differentiate between normal and abnormal values. Errors in RBF network analysis tend to be false negatives, and erroneous results tend to increase with increasing numbers of dimensions (e.g., numbers of sensors).

Using radial basis function networks and hyper-cubes for excursion classification in semi-conductor processing equipment


A request associated with a data item is received. A data grouping corresponding to the data item is identified. The identified data grouping belongs to a data grouping container that has been assigned a plurality of data groupings. Any one data grouping of the plurality of data groupings is individually reassignable to a different data grouping container. At least one data center where the identified data grouping is stored among a plurality of data centers is determined. A processing of the request is managed based on the determined data center that stores the identified data grouping.

Data centers are facilities used to store computer systems and components, such as data storage systems and their associated components. Modern data centers are typically large facilities whose computer systems, notably data storage systems, are used to store large amounts of data associated with users located throughout the world. The tremendous increase in the generation and consumption of data in recent times has been a catalyst for the utilization of more and more data centers around the world to store these vast amounts of data. Concerns relating to user dissatisfaction and legal liability associated with the loss of data have motivated the use of redundant data storage systems and have further contributed to the proliferation of data and the data centers needed to store such data. Organizing, accessing, and processing the enormous amounts of data and their redundant copies throughout the world is challenging. Users demand fast access to data irrespective of where the users are located in the world and irrespective of which data centers in the world actually contain the desired data. Faster access is associated with data access requests originating in the data center where the desired data is located. However, the data centers from which data access requests originate can vary over time, even for data accessed on behalf of a unique user. A change in the requesting data center can arise because the user travels from one region to another or because service workload is shifted from a data center with high loads to another with lower loads in order to lower service request response latencies. Therefore, there exists a need for a way to more efficiently organize, access, and process user data that is capable of being stored in data centers across the world.

Processing data groupings belonging to data grouping containers


A club head for a golf putter including a body portion having a top and a bottom, characterized in that the bottom has a horizontal surface at a central portion thereof, two first inclined surfaces extending upwardly from two sides of the horizontal surface, two second inclined surfaces extending upwardly from the two first inclined surfaces to the top, a third inclined surface extending upwardly from the horizontal surface and the first inclined surfaces, two first weights fitted into the body perpendicularly through the first inclined surfaces, and a second weight fitted into the body perpendicularly through the third inclined surface, whereby the user may strike the golf ball accurately.

1. Field of the Invention
This invention relates to a club head for a golf putter and in particular to one which can improve the striking stability and accuracy.
2. Description of the Prior Art
Referring to FIG. 1, the conventional club head 10 for a golf putter has a horizontal bottom 11, a curved toe 12 and a curved heel 13. However, it is very difficult to use such a golf putter to strike a golf ball to go along a path as desired, especially in uneven grass field.
Therefore, it is an object of the present invention to provide an improved club head for a golf putter which can obviate and mitigate the above-mentioned drawbacks.