Strong competition model with non-uniform dispersal in a heterogeneous environment

In this study, a strong competition model was considered between two species in a heterogeneous environment. For a system with two different constant diffusion rates for each competitor, the fast diffuser can be selected evolutionally under suitable assumptions if the competing interaction between the species is strong. We also claim that a strongly interacting competition leads to a more evolutionary selection than that with the same population dynamics if a species moves with a certain non-uniform dispersal. Furthermore, species with a certain non-uniform dispersal have a competitive advantage over linear random diffusers. In addition, a species with highly sensitive dispersal response to the environment may survive. These strongly competitive advantages were demonstrated by investigating the stability of semi-trivial solutions of the system with non-uniform dispersal and comparing it to the conditions of the model with constant diffusion.     

Group Hotelling's T^2 Test for Comparing Multiple Endpoints

Comparisons between two samples with multiple endpoints are often encountered in many real applications and Hotelling's T^2 test (HT) may suffer from loss of efficiency when multivariate normality assumption is violated. To overcome this issue, we propose a group Hotelling's T^2 test (GHT) where HT is conducted within each group after inverse normal transformation and then use the maximum value among combined statistics based on $p$-values at the group-level. Extensive simulations show that GHT is more robust than HT and some other existing procedures. Finally, the applications to plasma-renin activity in serum study and the ageing human brain further demonstrate the performance of GHT.     

Budget-constrained optimal insurance with belief heterogeneity

We re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a mild consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a simple two-part structure: full insurance on an event to which the insurer assigns zero probability, and a variable deductible on the complement of this event, which depends on the state of the world through a likelihood ratio. The latter is obtained from a Lebesgue decomposition of the insured’s belief with respect to the insurer’s belief.     

Enumerating words with forbidden factors

This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols 1 for given k, using generating function techniques that deserve to be better known.This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol 1 than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.     

Continuation of multiple power series in a sectorial domain

For multiple power series centered at the origin we consider the problem of its analytic continuability into a sectorial domain. The condition for continuability is formulated in terms of a holomorphic function that interpolates the series coefficients. For series in one variable this problem has been studied in the works of E. Lindelöf, N. Arakelian, and others.     

A HIV Infection Model with Periodic Multidrug Therapy

This paper investigates the effects of periodic drug treatment on a HIV infection model with two co-circulation populations of target cells. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable if R0 < 1, while the infection persists and there exists at least one positive periodic state when R0 > 1. Therefore, R0 serves as a threshold parameter for the infection. We then consider an optimization problem by shifting the phase of drug efficacy functions, which corresponds to change the dosage time of drugs in each time interval. It turns out that shifting the phase affect critically on the stability of the infection free steady state. Finally, exhaustive numerical simulations are carried out to support our theoretical analysis and explore the optimal phase shift.     

Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

An instrumentation system to measure the loads acting on the tractor PTO bearing during rotary tillage

Application of rotary tillage has been increased due to less tillage passes required, reduced draft, and greater efficiency through reduction in wheel slippage. Early failure of the bearing of tractor power take-off (PTO) shaft was observed in tractors of power range 30–35 horsepower during rotary tillage. An instrumentation setup involving an extended octagonal ring transducer (EORT) was developed and installed at the bottom of the bearing to measure the axial load and the vertical component of the radial load. The horizontal component of radial load was measured by strain gauges. Based on measured loads, the bearing life was assessed. Independent variables were: operating depth, number of blades, gear setting, engine speed, and tyre size. The average axial and radial loads varied from 786–3869 N, and 134–430 N, respectively. However, bearing experienced very high peak loads during each trial. The peak axial and radial loads was recorded between 1081–7534 N and 566–1794 N, respectively. The estimated bearing life based on peak loads was 171.98–28341.39 h. Based on the findings, it may be concluded that the average loads were not sufficient to cause quick failure of PTO bearing, rather sudden peak loads might be the root cause of early failure.     

Distributionally robust profit opportunities

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are considered. The infinite dimensional primal problems are formulated, leading to their simpler finite dimensional dual problems. A principal motivating question is how distributional ambiguity helps or hurts the robustness of the profit opportunity. Towards answering this question, some theory is developed and computational experiments are conducted. Finally some open questions and suggestions for future research are discussed.     

Hecke特征值相邻极大值的均值估计

取f为权为偶数k的全模群Γ=SL(2,Z)的Hecke特征型.定义λ_sym^mf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了∑_n≤x max{|λ_sym^mf(n)|^2β,|λ_sym^mf(n+h)|^2β}的上下界,其中h为一个固定的正整数,β> 0为一个正数.