Although the paper has two authors, I wish to exonerate my co-author D. L. Clements from responsibility for the need for these corrections; they affect an aspect of the paper in which he took no part. The first correction arises from neglecting, in the sixth line on p. 286, to exclude the less usual of the two possibilities occurring in Fredholm's Alternative. The other corrections are needed because the next two paragraphs claim that / + and /_, and fi and f2, have bounded first derivatives; the truth of these matters is expressed in (16.3) and (16.4) below, and entails the subsequent work given. To fill these gaps, I offer the following in place of the three complete paragraphs on p. 286. It should be remembered that we are discussing a special case of the general equations (1.1)—(1.3) considered in the paper: the case in which qi(r) = 0 = q2{r), n = 0 and a = \. Since 0<fc< 1, the kernels of (15.18) and (15.19) are continuous; and it is easily seen by power series expansions that the right-hand sides of these equations are also continuous in 0 ̂ x < k if suitably defined at x = 0. The equations consequently have unique continuous solutions for f+(x) and f-(x) in O^x^k subject to the condition \\K\\ < 1, which is sufficient to exclude the other Fredholm Alternative possibility. Table A (on p. 274) shows that ||^||<1 whenever a/6 «£ 0.86. But closer inequalities than (10.7) are possible; for instance, \\K\\ < 1 whenever a/b^0.99& can be proved as follows, when n = 0 and a = | . By (10.1), and (9.10) or (9.11),


—Image retrieval plays an important role in the analysis of obtained decisive visual information. The presence of visual inconsistency in visual appearance decreases the retrieval accuracy and many of the present retrieval methods emphasize single-source retrieval with the assumption of queries and databases distributions being similar. The number of features obtained with the traditional approach in which some of them are redundant, correlated, and sometimes noisy, increases the model feature space complexity and decreases interpretability. From the study of previous work, it is evident that feature fusion with cross-domain retrieval has not been addressed thoroughly so far. Thus, to deal with these issues, this extracts the optimal combination of the multi-modal features and fuses for enhancing retrieval accuracy. The complementary features obtained are effective with the traditional approach for the improvement of representation and retrieval effectiveness. Thus, Image Retrieval using Single and Cross-Domain Feature Fusion (SCDFF) is proposed in this work. The multi-modal features are extracted with Texture, Color, Statistical, and Scale Invariant Feature Transform (SIFT) descriptors to perform the retrieval process. The feature vector is fused using an optimized weight value which is obtained from Glowworm Swarm Optimization (GSO) algorithm and the image similarity is computed with K-Nearest Neighbor. An empirical analysis is performed to evaluate the proposed model and from the results obtained, it is evident that this work outperforms existing approaches in terms of accuracy. The novelty of this work lies in the fact of Single-Domain Feature Fusion (SDFF) and Cross-Domain Feature Fusion (CDFF) with optimization for Image Retrieval.


A device for separating a label sticker is provided to conveniently assemble and disassemble the device including a rolled label sticker paper. A device for separating a label sticker includes a bottom part(200), a first side surface(310), a first cover(500), a second cover(600), a second side surface(320), a guide part(360), a front surface, and a rear surface(420). A wounded roll is mounted on the bottom part. The first side surface is in contact with the bottom part via a first flap. The first cover has an opening(510) through which an end of the roll is extracted. The second cover is disposed on the first cover. The second side surface is in contact with a second flap. The guide part fixed a moving direction of a release paper. The front surface has grooves to be coupled to the guide part and the second cover. The rear surface corresponds to the front surface.


Collective dynamics is a complex emergence phenomenon yielded by local interactions within multi-agent systems. When agents cooperate or compete in the community, a collective behavior, such as consensus, polarization or diversity, may emerge. In this paper, we investigate a bipartite consensus process, in which all the agents converge to a final state characterized by identical modulus but opposite sign. Firstly, the interaction network of the agents is represented by a directed signed graph. A neighbor-based interaction rule is proposed for each agent with a single integrator dynamics. Then, we classify the signed network into heterogeneous networks and homogeneous networks according to the sign of edges. Under a weak connectivity assumption that the signed network has a spanning tree, some sufficient conditions are derived for bipartite consensus of multi-agent systems with the help of a structural balance theory. At the same time, signless Laplacian matrix and signed Laplacian matrix are introduced to analyze the bipartite consensus of multi-agent systems on homogeneous networks and heterogenous networks, respectively. Finally, simulation results are provided to demonstrate the bipartite consensus formation.


The detached housing has been a dominant housing in the past. With industrialization and urbanization, the detached housing has handed over its...