Some questions on integral geometry on noncompact symmetric spaces of higher rank

Let be a noncompact symmetric space of higher rank. We consider two types of averages of functions: one, over level sets of the heat kernel on and the other, over geodesic spheres. We prove injectivity results for functions in which extend the results in Pati and Sitaram (Sankya Ser A 62:419-424, 2000).

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression

Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p, r, t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p, r, t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t -> infinity. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.

Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

An integral fluctuation theorem for systems with unidirectional transitions

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where R-ij > 0 but R-ji = 0, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution, which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically and found to show the same qualitative features as systems exhibiting microreversibility.

THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4).

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Crack Tip Field and J-Integral with Strain Gradient Effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory Two typical crack Problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

¿Perspectiva médica o visión integral del hombre? : análisis crítico de la anticoncepción

Resumen: El objetivo principal de este trabajo es analizar si la anticoncepción es un asunto perteneciente a la Medicina, como lo indica la práctica, o si merece una visión bajo una perspectiva más amplia. Se analizan publicaciones que estudian el problema de la efectividad de la anticoncepción considerando variables demográficas, económicas y sociales que gravitan a la hora de evaluar la eficacia en anticoncepción. Se incluye en el análisis aspectos espirituales y psicológicos, que generalmente son subestimados, pero que fueron considerados en el pensamiento filosófico y antropológico que desplegó K. Wojtyla, quien parte de la base de la unidad de la persona

Estudio del comportamiento de plagas y enfermedades en el cultivo de cafe, mediante el uso de recuento integral Masatepe, Masaya

El estudio se realizó en el Centro de Capacitación y Servicio Regional Pacífico (Jardín Botánico) ubicado en la ciudad de Masatepe, Masaya, en el periodo comprendido entre Marzo del 2001 a Febrero del 2002. El objetivo fue evaluar la utilidad del recuento integral de plagas en el fortalecimiento de la toma de decisiones de manejo de plagas y enfermedades, de acuerdo al comportamiento que estas presentan en cada lote. Para la realización del trabajo se tomaron 10 lotes ya establecidos y en plena producción con diferentes manejo, distancias de siembra, niveles de sombra y variedades distintas. La metodología contempló 5 puntos por lote y 1O plantas por punto; tomando a cada una, variables de: número de hojas totales, número de hojas enfermas, número de frutos totales, número de frutos dañados. Las plagas y enfermedades con menor porcentaje de incidencia en general fueron: Minador (Leucoptera co.ffel/a Guerin), Cochinilla (Planoccocus citri L) y Antracnosis (Collectotrichum sp). Las acciones de manejo se establecerían de acuerdo a los niveles presentados, para los cuales se tomo el criterio de 10% para enfermedades foliares; 5% para enfermedades que afectan hojas y frutos; y el 5% para la Broca. Las plagas y enfermedades que se presentaron durante el estudio fueron: Roya, Mancha de Hierro, Antracnosis, Broca, Minador. Considerando a la mancha de Hierro y Broca como las de mayor importancia. El lote Catuai Rojo presentó la mayor incidencia de enfermedades afectado por: Roya (Hemileia Vastatrix, Berk y Br.) y Mancha de hierro (Cercospora co.ffeico/a Berk y cook.), el manejo implementado fue preventivo (podas sanitarias, selectivas y de recepo ). El lote con mayor incidencia de plaga, fue Salchicha Vegetal (SV), la acción de manejo implementadas fueron: la utilización de trampas semioquímicas y endosulfan.

Papel de la mecanización agrícola en el desarrollo integral de la sociedad. Elementos para la planificación de estrategias de mecanización. Un caso de estudio

La mecanización agrícola, como parte integral del desarrollo agropecuario de un país, tiene como fin contribuir a superar el déficit de alimentación, siempre y cuando, planificadores y políticos entiendan la dimensión de ésta como instrumento de desarrollo. Dicha estrategia será positiva si se toma en cuenta elementos primarios de cada región, como son: población, conocimientos, tradiciones culturales, características climáticas, al igual que aspectos que apoyan al desarrollo de los citados elementos, como son: créditos, instalaciones, infraestructuras, etc. La propuesta de mecanización debe involucrar productores, empresarios, industriales, beneficiarios, el gobierno en su papel de rector de las políticas a establecer y las instituciones de investigación, asesoría y prueba, como garantices de definición de los sistemas de producción y tecnología a implementar. Investigación realizada a finales de 1997, con el propósito de conocer el estado de la mecanización en la zona del pacíficcrsur de Nicaragua, indica que el nivel mas común de mecanización utiliza fuente de energía mixta: tracción motriz y animales de tiro. Utilizando fincas de tres extensiones, en presencia de cuatro cultivos, se realizo un análisis de rentabilidad de los tres niveles más utilizados, a partir del cual se propone una estrategia de mecanización.

Educación integral de la sexualidad de mujeres y de varones : desafío de nuestra época

La autora expone en el presente artículo algunos conceptos sobre sexualidad y las consideraciones que se deben tener en cuenta a la hora de educar a varones y a mujeres en el tema, teniendo en cuenta sus diferencias y peculiaridades corporales, psicoafectivas, espirituales y sociales. El objetivo para con los jóvenes es brindarles una visión integradora de la sexualidad, integrándola con el amor.