Homogeneity and local symmetry of complex (<Emphasis Type="Italic">κ</Emphasis>, µ)-spaces

We prove that a complex (κ, μ)-space with κ < 1 is a locally homogeneous complex contact metric manifold. Also, a complex (κ, μ)-space has either κ = 1 or is GH-locally symmetric.     

l-Proline catalyzed efficient one-pot three-component aza-Diels–Alder reactions on nitrostyrylisoxazoles: a facile synthesis of new isoxazolyl tetrahydroquinolines and isoxazolo[2,3-a]pyrimidines

l-Proline acts as an efficient organocatalyst and found to promote one-pot three-component aza-Diels–Alder reaction of aryl or isoxazole imines formed in situ from aromatic or isoxazoleamines and aromatic aldehydes with nitrostyrylisoxazoles to afford the isoxazolyl tetrahydroquinolines or isoxazolo[2,3-a]pyrimidines, respectively, in excellent yields at ambient temperature under neutral conditions.     

Floer–Novikov homology and applications to Lagrangian submanifolds

We use a non-Hamiltonian version of Lagrangian Floer homology to prove that an exact Lagrangian submanifold in the cotangent bundle of the 3-torus T ³ must be diffeomorphic to T ³. This improves a previous result of Fukaya, Seidel and Smith.     

Quantitative and Qualitative Analysis of the Anti-Proliferative Potential of the Pyrazole Scaffold in the Design of Anticancer Agents

The current work presents an objective overview of the impact of one important heterocyclic structure, the pyrazole ring, in the development of anti-proliferative drugs. A set of 1551 pyrazole derivatives were extracted from the National Cancer Institute (NCI) database, together with their growth inhibition effects (GI%) on the NCI’s panel of 60 cancer cell lines. The structures of these derivatives were analyzed based on the compounds’ averages of GI% values across NCI-60 cell lines and the averages of the values for the outlier cells. The distribution and the architecture of the Bemis–Murcko skeletons were analyzed, highlighting the impact of certain scaffold structures on the anti-proliferative effect’s potency and selectivity. The drug-likeness, chemical reactivity and promiscuity risks of the compounds were predicted using AMDETlab. The pyrazole ring proved to be a versatile scaffold for the design of anticancer drugs if properly substituted and if connected with other cyclic structures. The 1,3-diphenyl-pyrazole emerged as a useful scaffold for potent and targeted anticancer candidates.     

Placing a finite size facility with a center objective on a rectangular plane with barriers

This paper addresses the finite size 1-center placement problem on a rectangular plane in the presence of barriers. Barriers are regions in which both facility location and travel through are prohibited. The feasible region for facility placement is subdivided into cells along the lines of Larson and Sadiq [R.C. Larson, G. Sadiq, Facility locations with the Manhattan metric in the presence of barriers to travel, Operations Research 31 (4) (1983) 652–669]. To overcome complications induced by the center (minimax) objective, we analyze the resultant cells based on the cell corners. We study the problem when the facility orientation is known a priori. We obtain domination results when the facility is fully contained inside 1, 2 and 3-cornered cells. For full containment in a 4-cornered cell, we formulate the problem as a linear program. However, when the facility intersects gridlines, analytical representation of the distance functions becomes challenging. We study the difficulties of this case and formulate our problem as a linear or nonlinear program, depending on whether the feasible region is convex or nonconvex. An analysis of the solution complexity is presented along with an illustrative numerical example.     

Multirate multicast service provisioning II: a tâtonnement process for rate allocation

In multirate multicast different users in the same multicast group can receive services at different rates depending on their own requirements and the congestion level of the network. In this two-part paper we present a general framework for addressing the optimal rate control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. In Part II we present a market based mechanism and an adjustment process that have the following features. They satisfy the informational constraints imposed by the nature of multirate multicast; and when they are combined with the results of Part I they result in an optimal solution of the corresponding centralized multirate multicast problem.     

A desingularization theorem of Néron type

Summary LetA→A′ be a regular morphism between two noetherian rings. Then for everyA-algebra of finite typeB, everyA-morphism fromB toA′ can be factorised through aB-algebra of finite typeB′ which is standard (smooth) overA and which is ?as smooth as possible? overB (i.e. except above the singular locus ofB overA). This result is a positive answer to one conjecture due to M. Artin.

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Riassunto SiaA→A′ un omomorfismo regolare di anelli noetheriani. Si dimostra che per ogniA-algebraB di tipo finito, ogniA-omomorfismoB→A′ si può fattorizzare mediante unaB-algebraB′ di tipo finito che è liscia suA ed è ?la più liscia posibile? suB (più precisamente liscia suB meno il luogo singolare diB suA). Questo risultato è una risposta affermativa a una congettura di M. Artin.

     

Matrix analysis and the friedrichs operator of a quadrature domain

The Friedrichs operator of a quadrature domain is a finite rank operator which appears in the joint diagonalization of the Bergman space scalar product and its real part, regarded as a real symmetric form. This note relates some general aspects of the theory of pairs of hermitian or symmetric forms to the specific case of the Friedrichs operator.