Existence of solutions for a class of abstract differential equations with nonlocal conditions

We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. (C) 2010 Elsevier Ltd. All rights reserved.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

A new morphological variant of uterine PEComas with sex-cord-like pattern and WT1 expression: more doubts about the existence of uterine PEComas

PEComas are rare neoplasms that are sometimes associated with the tuberous sclerosis complex. They typically contain perivascular epithelioid cells that coexpress muscle and melanocytic markers. However, apart from these classical features, considerable clinical, pathologic, and immunohistochemical variation has been reported. WT1, the Wilms tumor gene product, can be expressed in various tumors from different anatomical sites, including sex-cord and other ovarian tumors with a sertoliform pattern. Neither a sex-cord like pattern nor WT1 expression has been described in PEComas. Here, we describe a case of uterine PEComa with a pattern of infiltration into the myometrium that is similar to stromal sarcomas, characterized by tongues and endovascular growing. The architecture and cellular morphology were similar to sex-cord tumors, and the PEComa was diffusely and strongly positive for WT1. We reviewed, from our files, an additional 9 cases of PEComa from different sites, and found WT1 expression in one more soft tissue tumor. We discuss the relationship between PEComas and other uterine sarcomas. (C) 2010 Elsevier Inc. All rights reserved.

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

The non-existence of a utility function and the structure of non-representable preference relations

In this paper we investigate the structure of non-representable preference relations. While there is a vast literature on different kinds of preference relations that can be represented by a real-valued utility function, very little is known or understood about preference relations that cannot be represented by a real-valued utility function. There has been no systematic analysis of the non-representation problem. In this paper we give a complete description of non-representable preference relations which are total preorders or chains. We introduce and study the properties of four classes of non-representable chains: long chains, planar chains, Aronszajn-like chains and Souslin chains. In the main theorem of the paper we prove that a chain is non-representable if and only it is a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. (C) 2002 Published by Elsevier Science B.V.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Children's metalinguistic activity in the construction of linguistic existence

In this paper we examine the construction of first entities in narratives produced by children of 5, 7, 10 years and adults1 . The study demonstrates that when children reformulate they try to construct entities detached from the situation of enunciation, which means that they construct a detached or a translated plane and they construct linguistic existence of entities. Entities must first be introduced into the enunciative space and then comments will be made in subsequent utterances. Constructing existence supposes extraction. This consists of “singling out an occurrence, that is, isolating and drawing its spatiotemporal boundaries” (Culioli, 1990, p. 182) . Once the occurrence of the notion is constructed (which means it has become a separate occurrence with situational properties), children can predicate about it. However, there are children who do not construct the linguistic existence of entities. I hypothesize that the mode of task presentation influences the success of constructing linguistic existence. Sharing the investigator’s knowledge about the stimulus images, children do not ascribe an existential status to the occurrence of the notional domain.

Amplification of the flgE gene provides evidence for the existence of a Brazilian borreliosis

INTRODUCTION: The symptoms of Brazilian borreliosis resemble the clinical manifestations of Lyme disease (LD). However, there are differences between the two in terms of epidemiological and laboratory findings. Primers usually employed to diagnose LD have failed to detect Borrelia strains in Brazil. OBJECTIVE: We aimed to identify the Brazilian Borrelia using a conserved gene that synthesizes the flagellar hook (flgE) of Borrelia burgdorferi sensu lato. METHOD: Three patients presenting with erythema migrans and positive epidemiological histories were recruited for the study. Blood samples were collected, and the DNA was extracted by commercial kits. RESULTS: The gene flgE was amplified from DNA of all selected patients. Upon sequencing, these positive samples revealed 99% homology to B. burgdorferi flgE. CONCLUSION: These results support the existence of borreliosis in Brazil. However, it is unclear whether this borreliosis is caused by a genetically modified B. burgdorferi sensu stricto or by a new species of Borrelia spp.

An existence result for discontinuous games

We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin (1986) and that it is neither implied nor does it imply the existence theorems of Baye, Tian, and Zhou (1993) and Reny (1999). Furthermore, we show that an equilibrium may fail to exist when, while maintaining weak payoff security, weak upper semicontinuity is weakened to reciprocal upper semicontinuity.

On the existence of pure-strategy equilibria in large games

Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler (1973), Rashid (1983), Mas-Colell (1984), Khan and Sun (1999) and Podczeck (2007a). The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games.

Managing innovation complexity: About the co-existence of innovation types

The purpose of this study is to contribute to the changing innovation management literature by providing an overview of different innovation types and organizational complexity factors. Aiming at a better understanding of effective innovation management, innovation and complexity are related to the formulation of an innovation strategy and interaction between different innovation types is further explored. The chosen approach in this study is to review the existing literature on different innovation types and organizational complexity factors in order to design a survey which allows for statistical measurement of their interactions and relationships to innovation strategy formulation. The findings demonstrate interaction between individual innovation types. Additionally, organizational complexity factors and different innovation types are significantly related to innovation strategy formulation. In particular, more closed innovation and incremental innovation positively influence the likelihood of innovation strategy formulation. Organizational complexity factors have an overall negative influence on innovation strategy formulation. In order to define best practices for innovation management and to guide managerial decision making, organizations need to be aware of the co-existence of different innovation types and formulate an innovation strategy to more closely align their innovation objectives.

The existence of only one haplotype of Leishmania major in the main and potential reservoir hosts of zoonotic cutaneous leishmaniasis using different molecular markers in a focal area in Iran

IntroductionLeishmania major is the causative agent of zoonotic cutaneous leishmaniasis (ZCL), and great gerbils are the main reservoir hosts in Iran. Abarkouh in central Iran is an emerging focal point for which the reservoir hosts of ZCL are unclear. This research project was designed to detect any Leishmania parasites in different wild rodent species.MethodsAll rodents captured in 2011 and 2012 from Abarkouh district were identified based on morphological characteristics and by amplification of the rodent cytochrome b (Cyt b) gene. To detect Leishmania infection in rodents, deoxyribonucleic acid (DNA) of each ear was extracted. Internal transcribed spacer-ribosomal deoxyribonucleic acid (ITS-rDNA), microsatellites, kinetoplast deoxyribonucleic acid (kDNA) and cytochrome b genes of Leishmania parasites were amplified by polymerase chain reaction (PCR). Restriction fragment length polymorphism (RFLP) and sequencing were employed to confirm the Leishmania identification.ResultsOf 68 captured rodents in the region, 55 Rhombomys opimus were identified and nine Leishmaniainfections (9/55) were found. In addition, eight Meriones libycus and two Tatera indicawere sampled, and one of each was confirmed to be infected. Two Meriones persicus and one Mus musculuswere sampled with no infection.ConclusionsThe results showed that all 11 unambiguously positive Leishmania infections were Leishmania major. Only one haplotype of L. major(GenBank access No. EF413075) was found and at least three rodents R. opimus, M. libycus and T. indica—appear to be the main and potential reservoir hosts in this ZCL focus. The reservoir hosts are variable and versatile in small ZCL focal locations.

Existence, multiplicity and behaviour of solutions of some elliptic differential equations of higher order

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009