On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in C-2 near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. Thisn condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range-roughly speaking-from being mildly infinite-type'' to very flat at the infinite-type points.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

House of the Infinite. Vt House, Cádiz 2014

On a marvelous place like a piece of earthly paradise, at Cádiz, we have built an infinite plane facing the infinite sea, the most radical house we have ever made.

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

Heat transfer with solid liquid phase change initiating at a point in a semi infinite mold

Short-time analytical solutions of temperature and moving boundary in two-dimensional two-phase freezing due to a cold spot are presented in this paper. The melt occupies a semi-infinite region. Although the method of solution is valid for various other types of boundary conditions, the results in this paper are given only for the prescribed flux boundary conditions which could be space and time dependent. The freezing front propagations along the interior of the melt region exhibit well known behaviours but the propagations along the surface are of new type. The freezing front always depends on material parameters. Several interesting results can be obtained as particular cases of the general results.

Cooling of an infinite slab in a two-fluid medium

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener - Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

The Supervised IBP: Neighbourhood Preserving Infinite Latent Feature Models

We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space.

Low threshold current density 1.5 mu m strained-MQW laser by n-type modulation-doping

1.5 mu m. n-type modulation-doping InGaAsP/InGaAsP strained multiple quantum wells grown by low pressure metalorganic chemistry vapor decomposition technology is reported for the first time in the world. N-type modulation-doped lasers exhibit much lower threshold current densities than conventional lasers with undoped barrier layers. The lowest threshold current density we obtained was 1052.5 A/cm(2) for 1000 mu m long lasers with seven quantum wells. The estimated threshold current density for an infinite cavity length was 94.72A/cm(2)/well, reduced by 23.3% compared with undoped barrier lasers. The n-type modulation doping effects on the lasing characteristics in 1.5 mu m devices have been demonstrated.

An organic-inorganic vanadium oxide with one-dimensional ladder-type structure: hydrothermal synthesis, structure and characterization of [V4O10(o-phen)(2)]

A novel organic-inorganic hybrid vanadium oxide [V4O10(o-phen)(2)], involving all vanadium atoms present in +5 oxidation, has been hydrothermally synthesized and characterized by elemental analysis, IR, UV-vis, ESR, XPS spectra and TG-DTA thermal analysis. The single-crystal X-ray diffraction shows that the red-brown crystal is formed in the triclinic system, space group P (1) over bar, a = 9.782(2), b = 6.5124(14), c = 19.765(4) Angstrom, alpha = 89.94(2)degrees, beta = 100.66(2)degrees, gamma = 89.86(2)degrees. The title compound exhibits an infinite one-dimensional ladder-type tetravanadate skeleton with organonitrogen donors of o-phenanthroline ligands coordinated directly to the vanadium oxide framework.

MODELED DIFFUSION-CONTROLLED RESPONSE AND RECOVERY BEHAVIOR OF A NAKED OPTICAL FILM SENSOR WITH A HYPERBOLIC-TYPE RESPONSE TO ANALYTE CONCENTRATION

The diffusion-controlled response and recovery behaviour of a naked optical film sensor (i.e., with no protective membrane) with a hyperbolic-type response [i.e., S0/S = (1 + Kc), where S is the measured value of the absorbance or luminescence intensity of one form of the sensor dye in the presence of the analyte, S0 is the observed value of S in the absence of analyte and K is a constant] to changes in analyte concentration, c, in a system under test is approximated using a simple model, and described more accurately using a numerical model; in both models it is assumed that the system under test represents an infinite reservoir. Each model predicts the variations in the response and recovery times of such an optical sensor, as a function of the final external analyte concentration, the film thickness (I) and the analyte diffusion coefficient (D). From an observed signal versus time profile for a naked optical film sensor it is shown how values for K and D/I2 can be extracted using the numerical model. Both models provide a qualitative description of the often cited asymmetric nature of the response and recovery for hyperbolic-type response naked optical film sensors. It is envisaged that the models will help in the interpretation of the response and recovery behaviour exhibited by many naked optical film sensors and might be especially apposite when the analyte is a gas.