Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Some regularity theorems for CR mappings

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.

EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.

Unraveling the Intricate Organization of Mammalian Mitochondrial Presequence Translocases: Existence of Multiple Translocases for Maintenance of Mitochondrial Function

Mitochondria are indispensable organelles implicated in multiple aspects of cellular processes, including tumorigenesis. Heat shock proteins play a critical regulatory role in accurately delivering the nucleus-encoded proteins through membrane-bound presequence translocase (Tim23 complex) machinery. Although altered expression of mammalian presequence translocase components had been previously associated with malignant phenotypes, the overall organization of Tim23 complexes is still unsolved. In this report, we show the existence of three distinct Tim23 complexes, namely, B1, B2, and A, involved in the maintenance of normal mitochondrial function. Our data highlight the importance of Magmas as a regulator of translocase function and in dynamically recruiting the J-proteins DnaJC19 and DnaJC15 to individual translocases. The basic housekeeping function involves translocases B1 and B2 composed of Tim17b isoforms along with DnaJC19, whereas translocase A is nonessential and has a central role in oncogenesis. Translocase B, having a normal import rate, is essential for constitutive mitochondrial functions such as maintenance of electron transport chain complex activity, organellar morphology, iron-sulfur cluster protein biogenesis, and mitochondrial DNA. In contrast, translocase A, though dispensable for housekeeping functions with a comparatively lower import rate, plays a specific role in translocating oncoproteins lacking presequence, leading to reprogrammed mitochondrial functions and hence establishing a possible link between the TIM23 complex and tumorigenicity.

Non-existence of tight neighborly triangulated manifolds with beta(1)=2

All triangulated d-manifolds satisfy the inequality ((f0-d-1)(2)) >= ((d+2)(2))beta(1) for d >= 3. A triangulated d-manifold is called tight neighborly if it attains equality in this bound. For each d >= 3, a (2d + 3)-vertex tight neighborly triangulation of the Sd-1-bundle over S-1 with beta(1) = 1 was constructed by Kuhnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with beta(1) = 2. In other words, there is no tight neighborly triangulation of (Sd-1 x S-1)(#2) or (Sd-1 (sic) S-1)(#2) for d >= 3. A short proof of the uniqueness of K hnel's complexes for d >= 4 under the assumption beta(1) not equal 0 is also presented.

Co-existence of tetragonal and monoclinic phases and multiferroic properties for x <= 0.30 in the (1-x)Pb(Zr0.52Ti0.48)O-3-(x)BiFeO3 system

Compositions with x <= 0.30 in the system (1- x)Pb(Zro(0.52)Ti(0.48))O-3-(x)BiFeO3 were synthesized by sol-gel method. Rietveld analysis of X-ray diffraction data reveals tetragonal structure (P4mm) for x <= 0.05 and monoclinic (Cm) phase along with the existence of tetragonal phase for 0.10 <= x <= 0.25 and monoclinic phase for x = 0.30. Transformation of E(2TO) and E + B1 vibrational modes in the range 210-250 cm(-1) (present for x <= 0.25) into A' + A `' modes at similar to 236 cm(-1) for x = 0.30, and occurrence of new vibrational modes A' and A `' in Raman spectra for x >= 0.10 unambiguously support the presence of monoclinic phase. Occurrence of remnant polarisation and enhanced magnetization with concentration of BiFeO3 indicates superior multiferroic properties. Variation of magneto-capacitance with applied magnetic field is a strong evidence of magneto-electric multiferroic coupling in these materials. (C) 2014 Elsevier B.V. All rights reserved.

Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

‘Neptune’ between ‘Hesperus’ and ‘Vulcan’: On descriptive names and non-existence

[EN]This work will focus on some aspects of descriptive names. The New Theory of Reference, in line with Kripke, takes descriptive names to be proper names. I will argue in this paper that descriptive names and certain theory in reference to them, even when it disagrees with the New Theory of Reference, can shed light on our understanding of (some) non-existence statements. I define the concept of descriptive name for hypothesised object (DNHO). My thesis being that DNHOs are, as I will specify, descriptions: a proposition expressed by the utterance ‘n is F’, where ‘n’ is a DNHO, is not singular at all; it is a descriptive proposition. To sum up, concerning proper names, the truth lies closer to the New Theory of Reference, but descriptivism is not altogether false. As for DNHOs descriptivism is, in some cases, the right fit.

Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.