Incompatibilism and the logic of transfer

Modal arguments for incompatibility of freedom and determinism are typically based on the “transfer principle” for inability to act otherwise (Beta). The principle of agglomerativity (closure under conjunction introduction) is derivable from Beta. The most convincing counterexample to Beta is based on the denial of Agglomeration. The defender of the modal argument has two ways to block counterexamples to Beta: (i) use a notion of inability to act otherwise which is immune to the counterexample to agglomerativity; (ii) replace Beta with a logically stronger principle Beta 2. I argue that the second strategy fails because the strengthened principle and Agglomeration together entail Beta. So this strategy makes sense only if Beta 2 is applied without Agglomeration. But if Beta 2 is used without Agglomeration, then the incompatibilist will undercut the rationale for the premise of his argument. I illustrate this point with the analysis of Warfield (1996) and his use of Beta 2 in the so called direct argument for incompatibilism.     

The Halász Inequality for Additive Function of Rational Argument

We obtain an upper bound for the quantity . Here I is an interval, is the set of rational numbers q=m/n I such that nx, and f(q) is an arbitrary real-valued additive function of rational argument. The interval I and function f may depend on x3.     

具有偏差变元的双曲型微分方程组解的振动性

本文获得了双曲型方程组在齐次Neumann,Dirichlet和Robin边值条件下,所有解振动的充分条件.     

A regularized trace formula and oscillation of eigenfunctions of a Sturm‐Liouville operator with retarded argument at 2 points of discontinuity

In this study, first, a formula for regularized sums of eigenvalues of a Sturm‐Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ...     

On existence and asymptotic behaviour of solutions of a fractional integral equation

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions, defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.     

MATHEMATICAL STUDY OF A PEST CONTROL MODEL INCORPORATING STERILE INSECT TECHNIQUE

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results.