The Bishop–Phelps–Bollobás theorem fails for bilinear forms on

In this paper we show that the Bishop–Phelps–Bollobás theorem fails for bilinear forms on l<sub>1sub>×l<sub>1sub>, while it holds for linear operators from l<sub>1sub> to l<sub>∞sub>.     

Bayesian Copulae Distributions, with Application to Operational Risk Management

The aim of this paper is to introduce a new methodology for operational risk management, based on Bayesian copulae. One of the main problems related to operational risk management is understanding the complex dependence structure of the associated variables. In order to model this structure in a flexible way, we construct a method based on copulae. This allows us to split the joint multivariate probability distribution of a random vector of losses into individual components characterized by univariate marginals. Thus, copula functions embody all the information about the correlation between variables and provide a useful technique for modelling the dependency of a high number of marginals. Another important problem in operational risk modelling is the lack of loss data. This suggests the use of Bayesian models, computed via simulation methods and, in particular, Markov chain Monte Carlo. We propose a new methodology for modelling operational risk and for estimating the required capital. This methodology combines the use of copulae and Bayesian models.      

Application of Rouche’s theorem for MP filter design

The method for the minimum-phase (MP) finite impulse response (FIR) filter design, based on Rouche&rsquo;s theorem from complex analysis is presented here. The filter is designed directly from a given specification. The method uses the cosine filters and the sharpening technique resulting in a multiplierless filter.     

攀登伪蒙特卡罗积分法在Sobolev和Korobov空间中的随机化误差

攀登伪蒙特卡罗积分法是由伪蒙特卡罗与蒙特卡罗方法混合而成的一种新方法，它体现了两者的优点．本文研究这种积分法在Sobolev空间和Korobov空间中的随机化误差．我们证明攀登(λ，t，m，s)-网积分法在这两个空间中的随机化误差的渐近阶为n^3/2[logn]^(s-1)/2。     

On effectively computable realizations of choice functions: Dedicated to Professors Kenneth J. Arrow and Anil Nerode

Let X be a compact, convex subset of R<sub>nsub>, and let be a recursive space of alternatives, where R(X) is the image of X in a recursive metric space, and is the family of all recursive subsets of R(X). If is a non-trivial recursively representable choice function that is rational in the sense of Richter, we prove that C has no recursive realization within Church's Thesis. Our proof is not a diagonalization argument and uses no paradoxical statements from formal systems. Instead, the proof is a Kleene-Post reduction style argument and uses the Turing equivalence between mechanical devices of computation and the recursive functions of Gödel and Kleene.     

A new approach to constant term identities and Selberg-type integrals

Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero&ndash;Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.     

生态平衡制约下离散尺度结构种群的最优收获

研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构.     

Existence of positive periodic solutions for a generalized Nicholson’s blowflies model

In this paper, by using the Krasnoselskii cone fixed point theorem, we obtain a sufficient condition as well as a necessary condition for the existence of positive periodic solutions of the following generalized Nicholson&rsquo;s blowflies model:

ss="formula" id=">

ss="mathml">ss="imgLazyJSB inlineImage" height="37" width="372" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042707005912-si1.gif">script>style="vertical-align:bottom" width="372" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0377042707005912-si1.gif">script>ss="quad">space>t≥0.ss="temp" src="/sd/blank.gif">

In the degenerate case, i.e.,&nbsp;where the coefficients and delays of the above equation are all constants, a sufficient and necessary condition for the existence of positive periodic solutions is obtained. Our results are completely new, and generalize and improve some results from the literature.     

Generalized Hirano inverses in rings

We introduce and study a new class of generalized inverses in rings. An element a in a ring R has generalized Hirano inverse if there exists <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0001.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0001.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />scroll" altimg="eq-00001.gif">b∈Rspan> such that <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0002.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0002.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />scroll" altimg="eq-00002.gif">bab=b,b∈comsup>m2sup>stretchy="false">(astretchy="false">),sup>a2sup>?ab∈sup>Rqnilsup>.span> We prove that the generalized Hirano inverse of an element is its generalized Drazin inverse. An element <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0003.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0003.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />scroll" altimg="eq-00003.gif">a∈Rspan> has generalized Hirano inverse if and only if there exists <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0004.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0004.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />scroll" altimg="eq-00004.gif">p=sup>p2sup>∈comsup>m2sup>stretchy="false">(astretchy="false">)span> such that <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0005.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lagb20/2019/lagb20.v047.i07/00927872.2018.1546391/20190531/images/lagb_a_1546391_ilm0005.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />scroll" altimg="eq-00005.gif">sup>a2sup>?p∈sup>Rqnilsup>span>. We then completely determine when a 2?×?2 matrix over projective-free rings has generalized Hirano inverse. Cline’s formula and additive properties for generalized Hirano inverses are thereby obtained.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate s="true">s="true">s="true">Ds="true">s="true">psup> functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy s="true">s="true">s="true">Ds="true">s="true">psup> functions by s="true">s="true">s="true">Vs="true">s="true">psup> ones.