Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...

State-of-the-art first-order automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has...

Purpose A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement resulting system differential algebraic equations reformulated into ordinary (ODE). The ODE integrated in time by explicit integration schemes. purpose this pape...

This paper presents two views of stepwise enhancement, one a pragmatic syntax-based approach and the other a semantic approach based on higher-order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. By combining the advantages of both approaches, it is shown how more code in both functional and...

In the exact propagator for finite temperature gluons the location of the transverse and longitudinal poles in the gluon propagator are unknown functions of wave vector: ωT (k) and ωL(k). The residues of the poles, also unknown, fix the normalization of the one gluon vector potential and thus of the field strength. The naive energy density ~ E · ~ D + ~ B · ~ H is not correct because of dispers...