Narrow Results

In equitable multiobjective optimization, all of the objectives are uniformly optimized, but in some cases, the decision maker believes that some of them should be uniformly optimized. In order to solve the proposed problem, we introduce the concept of equitable $A_P$-efficiency, where $P=\{P_1,P_2,\dots ,P_n\}$ is a partition of the index set of objective functions and the preference matrix $A_P$ is the direct sum of the matrices $A_1,A_2,\dots ,A_n$, in which $A_k$ is a preference matrix for the objective functions in the class $P_k$ for $k=1,2,\dots ,n$. We examine some theoretical and practical aspects of equitably $A_P$-efficient solutions and provide the some conditions that guarantee the relation of equitable $A_P$-dominance is a $P$-equitable rational preference.

Furthermore, we introduce the new problem with the preference matrix $A_P$ and we decompose it into a collection of smaller subproblems. In continuation, the subproblems are solved by the concept of equitable efficiency. Finally, two models are demonstrated to coordinate equitably efficient solutions of the proposed subproblems.

Imaging technology has undergone extensive development since 1985, which has practical implications concerning civilians and the military. Recently, image fusion is an emerging tool in image processing that is adept at handling diverse image types. Those image types include remote sensing images and medical images for upgrading the information through the fusion of visible and infrared light based on the analysis of the materials used. Presently, image fusion has been mainly performed in the medical industry. With the constraints of diagnosing a disease via single-modality images, image fusion could be able to meet up the prerequisites. Hence, it is further suggested to develop a fusion model using different modalities of images. The major intention of the fusion approach is to achieve higher contrast, enhancing the quality of images and apparent knowledge. The validation of fused images is done by three factors that are: (i) fused images should sustain significant information from the source images, (ii) artifacts must not be present in the fused images and (iii) the flaws of noise and misregistration must be evaded. Multimodal image fusion is one of the developing domains through the implementation of robust algorithms and standard transformation techniques. Thus, this work aims to analyze the different contributions of various multimodal image fusion models using intelligent methods. It will provide an extensive literature survey on image fusion techniques and comparison of those methods with the existing ones. It will offer various state-of-the-arts of image fusion methods with their diverse levels as well as their pros and cons. This review will give an introduction to the current fusion methods, modes of multimodal fusion, the datasets used and performance metrics; and finally, it also discusses the challenges of multimodal image fusion methods and the future research trends.

Let $K_n$ denote a complete graph on $n$ vertices and $S_k$ denote a complete bipartite graph $K_{1,k}$. A Bowtie $B_l$ is a graph formed by the union of two cycles $C_n$ and $C_m$ intersecting at a common vertex. A decomposition of a graph $G$ is a collection of edge-disjoint subgraphs $H$, such that every edge of G belongs to exactly one $H$. Given non-isomorphic subgraphs $H_1$ and $H_2$ of $G$, a $(H_1,H_2)$ — multi-decomposition of $G$ is the decomposition of $G$ into $a$ copies of $H_1$ and $b$ copies of $H_2$, such that $a{H}_1\oplus b{H}_2=G$, for some integers $a,b\ge 0$. In this paper, the multi-decomposition of $K_n$ into $S_k$ and $B_l$ has been investigated and obtained a necessary and sufficient condition when $k=l=6$. It is proved that for a given positive integer $n$, $K_n$ can be decomposed into $a$ copies of $S_6$ and $b$ copies of $B_6$ for some pair of non-negative integers $(a,b)$ if and only if $6(a+b)=\left(\genfrac{}{}{0.0pt}{}{n}{2}\right)$, for all $n\ge 9$.

Weighted multioperator tree automata (for short: wmta) are finite-state bottom-up tree automata in which the transitions are weighted with an operation taken from some multioperator monoid. A wmta recognizes a tree series which is a mapping from the set of trees to some commutative monoid. We prove that every wmta recognizable tree series can be decomposed into a relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta; vice versa, the composition of an arbitrary relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta yields a wmta recognizable tree series. We use this characterization result for specific multioperator monoids and prove (1) a new decomposition of polynomial bottom-up tree series transducers over semirings and (2) a new characterization of tree series which are recognizable by weighted tree automata over semirings, in terms of projections of local tree languages.

This paper presents evidence that since 1980, relative to native-born Americans and other immigrants, the earnings of Taiwanese immigrants have grown rapidly as they assimilate into the U.S. economy. Consistent with the existing U.S. evidence, I show that most of the immigrant–native earnings gaps can be explained by endowments, and the importance of endowments continues to increase. The estimates indicate that the improved endowments from education and U.S. experience, along with rising returns to both factors, largely explain Taiwanese immigrants’ economic assimilation experience. I show that more recently arrival cohorts of Taiwanese immigrants have earned more than the older ones since 1980.

This paper estimates the gender wage gap and its composition in China’s urban labor market. The traditional Blinder–Oaxaca (1973) decomposition method with different weighing systems is employed. To correct for potential selection bias caused by women’s labor force participation, we employ the Heckman’s two-step procedure to estimate the female wage function. A large proportion of the gender wage gap is unexplained by differences of productive characteristics of individuals. Even though women have higher level of education attainments on average, they receive lower wages than men. Both facts suggest a potential discrimination against women in China.

We analyze the consumption inequality in India among different caste groups namely SC, ST, OBC and Others using three rounds of Household Level Consumption Expenditure Survey Data from 1993–94 to 2009–10. Regression analysis shows disparity in consumption expenditure across various caste groups. Values of Gini coefficient, Theil’s Index and overlapping index display an increasing trend in both within- and between-group inequality over time. The possibility of stratification among “Others” is identified. It is found that SCs and STs in particular bear the burden of increasing inequality, indicating possible inefficient implementation of the welfare schemes aimed at these communities.

This paper examines the pattern and evolution trend of foreign investment in China through combining decomposition analysis and framework of transitional dynamics. It is recognized that inter-regional disparity contributes the most to China’s disparity in foreign investment. Stochastic kernel analyses are then performed for the country and the economic zones regarding the foreign investment trend. It is concluded that convergence of foreign investment to the country’s mean cannot be attained and continues to locate at the lower end. This analysis offers illuminating insights on the evolution of foreign investment in China across time.

The study examines the extent of gender- and caste-based discrimination among the formally and informally employed in India using the National Sample Survey Office (NSSO) Employment-Unemployment Survey (EUS) data for the four major rounds from 1999–00 to 2011–12. Oaxaca-Blinder decomposition results corrected for self-selection show wage discrimination to be significantly higher in informal employment compared to the formally employed. Similarly, caste-based discrimination is found to be lower compared to gender-based discrimination. The quantile decomposition results show discrimination to vary across the quantiles. Our results highlight the need for better regulation of the informal labor market in India.

Based on the decomposition of SU(2) gauge field, we derive a generalization of the decomposition theory for the SU(N) gauge field. We thus obtain the invariant electromagnetic tensors of SU(N) groups and the extended Wu–Yang potentials. The sourceless solutions are also discussed.

In this paper, we apply decomposition to orbifolds with quantum symmetries to resolve anomalies. Briefly, it has been argued by, e.g. Wang–Wen–Witten, Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the orbifold group so that the pullback of the anomaly to the larger orbifold group is trivial. For this procedure to resolve the anomaly, one must specify a set of phases in the larger orbifold, whose form is implicit in the extension construction. There are multiple choices of consistent phases, which give rise to physically distinct resolutions. We apply decomposition, and find that theories with enlarged orbifold groups are equivalent to (disjoint unions of copies of) orbifolds by nonanomalous subgroups of the original orbifold group. In effect, decomposition implies that enlarging the orbifold group is equivalent to making it smaller. We provide a general conjecture for such descriptions, which we check in a number of examples.

In this paper, we discuss decomposition in the context of three-dimensional Chern–Simons theories. Specifically, we argue that a Chern–Simons theory with a gauged noneffectively-acting one-form symmetry is equivalent to a disjoint union of Chern–Simons theories, with discrete theta angles coupling to the image under a Bockstein homomorphism of a canonical degree-two characteristic class. On three-manifolds with boundary, we show that the bulk discrete theta angles (coupling to bundle characteristic classes) are mapped to choices of discrete torsion in boundary orbifolds. We use this to verify that the bulk three-dimensional Chern–Simons decomposition reduces on the boundary to known decompositions of two-dimensional (WZW) orbifolds, providing a strong consistency test of our proposal.

It was recently argued by Nguyen, Tanizaki and Ünsal that two-dimensional pure Yang–Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper, we compare this decomposition to the Gross–Taylor expansion of two-dimensional pure $SU(N)$ Yang–Mills theory in the large-$N$ limit as the string field theory of a sigma model. Specifically, we study the Gross–Taylor expansion of individual Nguyen–Tanizaki–Ünsal universes. These differ from the Gross–Taylor expansion of the full Yang–Mills theory in two ways: a restriction to single instanton degrees, and some additional contributions not present in the expansion of the full Yang–Mills theory. We propose to interpret the restriction to single instanton degrees as implying a constraint, namely that the Gross–Taylor string has a global (higher-form) symmetry with Noether current related to the worldsheet instanton number. We compare two-dimensional pure Maxwell theory as a prototype obeying such a constraint, and also discuss in that case an analogue of the Witten effect arising under two-dimensional theta angle rotation. We also propose a geometric interpretation of the additional terms, in the special case of Yang–Mills theories on 2-spheres. In addition, also for the case of theories on 2-spheres, we propose a reinterpretation of the terms in the Gross–Taylor expansion of the Nguyen–Tanizaki–Ünsal universes, replacing sigma models on branched covers by counting disjoint unions of stacky copies of the target Riemann surface, that makes the Nguyen–Tanizaki–Ünsal decomposition into invertible field theories more nearly manifest. As the Gross–Taylor string is a sigma model coupled to worldsheet gravity, we also briefly outline the tangentially related topic of decomposition in two-dimensional theories coupled to gravity.

Density functional theory method is used to explore the mechanism of dissociative adsorption of methane (CH₄) on S_A type stepped Si(100) surface. Two reaction paths are described that produce CH₃ and hydrogen atom fragments adsorbed on the dimer bonds present on each terraces. It has been found that, in the initial stage of the carbonization of stepped Si(100) surface, the CH₃ and H fragments bound to the Si dimer atoms by following the first reaction path.

Over the last 15 years, there has been rapid growth in applications of time-reversal symmetry of wave propagation to enhance communications and imaging through highly scattering media. These techniques exploit both temporal and spatial reciprocity to mitigate signal distortion created from the large number of independent propagation paths between a transmitter and receiver. The time-reversal process is often described by the time-reversal operator (TRO), or equivalently by the multistatic response matrix (MRM), defined by the transmit and receive system. A singular value decomposition of this operator (or MRM) is the starting point for many of the time-reversal imaging techniques. In addition to imaging, this decomposition can also be used to extract information about objects embedded within the propagation medium, i.e., target characterization. In this paper, we review the development of target characterization in time-reversal, with an emphasis on extracting information from small targets. We will analyze the MRM for both acoustic and electromagnetic scattering and show how the symmetry of the target is reflected in the properties of the singular value spectrum. Finally, we discuss several open problems and potential applications.

According to both the first principle and materials chemistry, a method for fabricating [(Ca_1-xSr_x)_2-2y](Ti_2-2yLi_2y)Si_2yO_6-y ceramic was investigated. It was considered that the sintering was promoted by self-accelerated diffusion due to the formation of point defects caused by doping with Li₂Si₂O₅. Consequently, a concept of non-stoichiometrically activated sintering, which was enhanced by point defects without the help of a grain boundary phase, was systematically studied in the Ca_1-xSr_xTiO_3-Li₂Si₂O₅ system. The mechanical and dielectric properties of [(Ca_1-xSr_x)_2-2y](Ti_2-2yLi_2y)Si_2yO_6-y were greatly enhanced by adding Li₂Si₂O₅. To improve CO₂ decomposition activity, [(Ca_1-xSr_x)_2-2y](Ti_2-2yLi_2y)Si_2yO_6-y, which possesses both high permittivity and high dielectric strength was used as a dielectric barrier to decompose CO₂ by dielectric barrier discharges (DBDs) plasma without using any catalyst and auxiliary substance. It successfully generated DBDs plasma and the CO₂ conversion was much higher than that using an alumina or a silica glass barrier which was widely used as the dielectric barrier in previous studies.

A coupled 2+1-dimensional discrete Chen–Lee–Liu equation is proposed, which together with two 1+1-dimensional discrete Kaup–Newell equations is decomposed into solvable ordinary differential equations with the help of the resulting Lax matrix and its finite-order expansion. Based on the theory of the algebraic curve, the Abel–Jacobi coordinates are introduced to straighten out the corresponding continuous flow and discrete flow, by which explicit solutions for the coupled 2+1-dimensional discrete Chen–Lee–Liu equation and the 1+1-dimensional discrete Kaup–Newell equations are obtained in the Abel–Jacobi coordinates.

In this paper, we investigate an integrable nonlocal “breaking soliton” equation, which can be decomposed into the nonlocal nonlinear Schrödinger equation and the nonlocal complex modified Korteweg–de Vries equation. As an application, with the use of this decomposition and Darboux transformation, the dark solitons, antidark solitons, rational dark solitons and rational antidark solitons of the considered equation are given explicitly. In particular, the interaction mechanisms of these solutions are discussed and illustrated through some figures.

Vegetable insulating oil, with advantages such as high safety and environmental friendliness, is a good substitute for traditional mineral oil. However, thermal failure is one of the important factors affecting the safe operation of oil-immersed electrical equipment. This study focuses on soybean vegetable oil as the research subject and establishes a simulation model for soybean insulating oil to investigate the influence of thermal stress at different temperatures ranging from 1000K to 2000K on system decomposition and gas generation characteristics. The results indicate that, under elevated temperatures, the decomposition of soybean vegetable insulating oil predominantly occurs through decarboxylation reactions, leading to the generation of CO₂ and hydrocarbon radicals. The hydrocarbon radicals further decompose and react with other species, resulting in the formation of characteristic gases. It was observed that CO₂ and C₂H₄ serve as stable thermal decomposition by-products. Increasing temperatures significantly enhance the generation rates of various characteristic products and broaden the variety of such products. For instance, H₂ and CH₄ are characteristic gases produced at different temperature ranges. Studying the decomposition and gas generation characteristics of vegetable insulating oil under thermal stress holds crucial significance for transformer design and operation.

This paper proposes a new approach to improve multiclass classification performance by employing Stacked Generalization structure and One-Against-One decomposition strategy. The proposed approach encodes the outputs of all pairwise classifiers by implicitly embedding two-class discriminative information in a probabilistic manner. The encoded outputs, called Meta Probability Codes (MPCs), are interpreted as the projections of the original features. It is observed that MPC, compared to the original features, has more appropriate features for clustering. Based on MPC, we introduce a cluster-based multiclass classification algorithm, called MPC-Clustering. The MPC-Clustering algorithm uses the proposed approach to project an original feature space to MPC, and then it employs a clustering scheme to cluster MPCs. Subsequently, it trains individual multiclass classifiers on the produced clusters to complete the procedure of multiclass classifier induction. The performance of the proposed algorithm is extensively evaluated on 20 datasets from the UCI machine learning database repository. The results imply that MPC-Clustering is quite efficient with an improvement of 2.4% overall classification rate compared to the state-of-the-art multiclass classifiers.