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Hamming distance of a two bit strings u and v of length n is defined to be the number of positions of u and v with different digit. If G is a simple graph on n vertices and m edges and B is an edge–vertex incidence matrix of G, then every edge e of G can be labeled using a binary digit string of length n from the row of B which corresponds to the edge e. We discuss Hamming distance of two different edges of the graph G. Then, we present formulae for the sum of all Hamming distances between two different edges of G, particularly when G is a path, a cycle, and a wheel, and some composite graphs.

The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The authors establish a result concerning the L²-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

Canada criminalized the nonconsensual distribution of intimate images in 2014. Lawmakers and commentators noted that this new offense would fill a legislative gap in relation to “revenge pornography,” which entails individuals (typically men) sharing intimate images of their ex-partners (typically women) online in an attempt to seek revenge or cause them harm. Feminist writers and activists categorize revenge pornography as a symptom and consequence of “rape culture,” in which sexual violence is routinely trivialized and viewed as acceptable or entertaining, and women are blamed for their sexual victimization. In this chapter, I analyze Canada's burgeoning revenge pornography case law and find that these cases support an understanding of revenge pornography as a serious form of communal, gendered, intimate partner violence, which is extremely effective at harming victims because of broader rape culture. While Canadian judges are taking revenge pornography seriously, there is some indication from the case law that they are at risk of relying on gendered reasoning and assumptions previously observed by feminists in sexual assault jurisprudence, which may have the result of bolstering rape culture, rather than contesting it.

We explore the impact of equity liquidity on a firm’s dynamic leverage adjustments and the moderating impacts of leverage deviation and target instability on the link between equity liquidity and dynamic leverage in the UK market.

In applying the two-step system GMM, we estimate our model by exploring suitable instruments for the dynamic variable(s), i.e. lagged values of the dynamic term(s).

Our analyses document that a firm’s equity liquidity has a positive impact on the speed of adjustment (SOA) of its leverage ratio back to the target ratio in the UK market. We also demonstrate that the positive relationship between liquidity and SOA is more pronounced for firms whose current position is relatively close to their target leverage ratio and whose target ratio is relatively stable.

This study provides important implications for both firms’ managers and investors. Particularly, firms’ managers who wish to increase the leverage SOA to enhance firms’ value need to give great attention to their equity liquidity. Investors who want to evaluate firms’ performance could also consider their equity liquidity and leverage SOA.

We are the first to enrich the literature on leverage adjustments by identifying equity liquidity as a new determinant of SOA in a single developed country with many differences in the structure and development of capital markets, ownership concentration and institutional characteristics. We also provide new empirical evidence of the joint effect of equity liquidity, leverage deviation and target instability on leverage SOA.

This paper measures different market risk impacts on options portfolios under the new Fundamental Review of the Trading Book (FRTB) regulation, issued in Basel and coming into effect in 2023.

This paper first suggests an algorithm for implementing the FRTB standardised approach via the sensitivities-based method to estimate a portfolio's risk capital and presents an illustration applied to an option position. Second, it proposes a methodology to estimate the expected shortfall in options portfolios from the FRTB internal models approach. In this regard, an application is developed to measure expected shortfall (ES) and value at risk (VaR) impacts under FRTB versus conventional VaR in a currency option position by considering stress scenarios from the 2007–9 and 2020–1 crises and back-testing procedures.

The suggested algorithm satisfactorily captures impacts via the sensitivities-based method, and higher risk capital demands are expected for emerging economies. Also, the planned FRTB methodology to measure ES and VaR is appropriate; in particular, historical metrics perform well. Astonishingly, their revealed impacts are more significant under the 2020–1 pandemic crisis than the 2007–9 financial crisis.

The proposals developed weave a communication bridge between the standardised and internal approaches of FRTB regulation, which can be scaled up technologically and institutionally.

In this paper, the authors study the production and pricing decisions of a remanufacturing supply chain composed of a supplier, an assembler and a remanufacturer, in which the remanufacturing of components requires patent licensing from the supplier.

The authors consider three different models with government subsidy for remanufacturing: (1) no government subsidies; (2) the government subsidizes the remanufacturing behavior of the supplier and (3) the government subsidizes the remanufacturing behavior of the remanufacturer and use the Stackelberg game model to solve and analyze the equilibrium wholesale prices of components and the equilibrium outputs of new and remanufactured products under three subsidy modes.

The results show that the equilibrium wholesale prices of two kinds of components decrease with the unit patent licensing fee and the unit government subsidy, and the equilibrium quantity of the remanufactured products under the three modes is obviously higher than that of the new products.

Finally through numerical simulation, it is found that the equilibrium profits of the supplier, the manufacturer and the supply chain increase monotonously in relation to the unit government subsidy, while the optimal profit of the assembler in relation to the unit government subsidy tends to decrease first and then increase.

This paper aims to study Irreversible conversion processes, which examine the spread of a one way change of state (from state 0 to state 1) through a specified society (the spread of disease through populations, the spread of opinion through social networks, etc.) where the conversion rule is determined at the beginning of the study. These processes can be modeled into graph theoretical models where the vertex set V(G) represents the set of individuals on which the conversion is spreading.

The irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process which starts by choosing a set S_0?V, and for each step t (t = 1, 2,…,), S_t is obtained from S_(t−1) by adjoining all vertices that have at least k neighbors in S_(t−1). S_0 is called the seed set of the k-threshold conversion process and is called an irreversible k-threshold conversion set (IkCS) of G if S_t = V(G) for some t = 0. The minimum cardinality of all the IkCSs of G is referred to as the irreversible k-threshold conversion number of G and is denoted by C_k (G).

In this paper the authors determine C_k (G) for generalized Jahangir graph J_(s,m) for 1 < k = m and s, m are arbitraries. The authors also determine C_k (G) for strong grids P_2? P_n when k = 4, 5. Finally, the authors determine C_2 (G) for P_n? P_n when n is arbitrary.

This work is 100% original and has important use in real life problems like Anti-Bioterrorism.

The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations x(6)+(1+p2+q2)x… .+(p2+q2+p2q2)x¨+p2q2x=εF(x,ẋ,x¨,x…,x… .,x(5)), where p and q are rational numbers different from 1, 0, −1 and p ≠ q, ε is a small enough parameter and F ∈ C² is a nonlinear autonomous function.

The authors shall use the averaging theory to study the periodic solutions for a class of perturbed sixth-order autonomous differential equations (DEs). The averaging theory is a classical tool for the study of the dynamics of nonlinear differential systems with periodic forcing. The averaging theory has a long history that begins with the classical work of Lagrange and Laplace. The averaging theory is used to the study of periodic solutions for second and higher order DEs.

All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results.

The authors studied Equation 1 which depends explicitly on the independent variable t. Here, the authors studied the autonomous case using a different approach.

This paper aims to investigate the effect of product-related description abstractness/concreteness on perceived trustworthiness and the role of consumer product expertise and shopping-stage mindset in the persuasiveness of abstract vs concrete product descriptions.

Two online experiments were conducted: Study 1 (description abstractness – manipulated between-subject; consumer product expertise, perceived trustworthiness, purchase intent – measured), Study 2 (consumer shopping-stage mindset – manipulated between-subject; description abstractness – manipulated within-subject; consumer product expertise, perceived trustworthiness, abstract/concrete description preference – measured).

The negative effect of the abstractness (abstract descriptions vs the ones supplemented with relevant product details) on description trustworthiness was evidenced in Study 1. Trustworthiness was positively related to purchase intent, especially for high product expertise. Study 2 replicated the effect of product description abstractness on its trustworthiness in terms of two other forms of abstractness (abstract descriptions vs the ones supplemented with irrelevant product details and product benefits vs attributes). The goal-oriented (vs comparative) mindset had a positive effect on the benefit (vs attribute) description preference, especially for high product expertise.

For marketers, the results suggest the positive consequences of presenting concrete information on product attributes and the conditions enhancing the effectiveness of presenting product benefits.

The paper integrates the existing views on consumer response to abstract vs concrete information (lexical abstractness/concreteness, means-end chain theory) and links them to consumer product expertise and shopping-stage mindset.