ALBERT

Beschreibung: We consider two principal bundles of embeddings with total space E m b ( M , N ) , with structure groups D i f f ( M ) and D i f f + ( M ) , where D i f f + ( M ) is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: B ( M , N ) = E m b ( M , N ) / D i f f ( M ) and B + ( M , N ) = E m b ( M , N ) / D i f f + ( M ) from the various properties described, an adequate group seems to be a group of Fourier integral operators, which is carefully studied. It is the main goal of this paper to analyze this group, which is a central extension of a group of diffeomorphisms by a group of pseudo-differential operators which is slightly different from the one developped in the mathematical litterature e.g. by H. Omori and by T. Ratiu. We show that these groups are regular, and develop the necessary properties for applications to the geometry of B ( M , N ) . A case of particular interest is M = S 1 , where connected components of B + ( S 1 , N ) are deeply linked with homotopy classes of oriented knots. In this example, the structure group of the tangent space T B + ( S 1 , N ) is a subgroup of some group G L r e s , following the classical notations of (Pressley, A., 1988). These constructions suggest some approaches in the spirit of one of our previous works on Chern-Weil theory that could lead to knot invariants through a theory of Chern-Weil forms.

Beschreibung: Analytical solutions are developed to work out the two-dimensional (2D) temperature changes of flow in the passages of a plate heat exchanger in parallel flow and counter flow arrangements. Two different flow regimes, namely, the plug flow and the turbulent flow are considered. The mathematical formulation of problems coupled at boundary conditions are presented, the solution procedure is then obtained as a special case of the two region Sturm-Liouville problem. The results obtained for two different flow regimes are then compared with experimental results and with each other. The agreement between the analytical and experimental results is an indication of the accuracy of solution method.

Beschreibung: We consider a mosquito-borne epidemic model, where the adoption by individuals of insecticide–treated bed–nets (ITNs) is taken into account. Motivated by the well documented strong influence of behavioral factors in ITNs usage, we propose a mathematical approach based on the idea of information–dependent epidemic models. We consider the feedback produced by the actions taken by individuals as a consequence of: (i) the information available on the status of the disease in the community where they live; (ii) an optimal health-promotion campaign aimed at encouraging people to use ITNs. The effects on the epidemic dynamics of each of these feedback are assessed and compared with the output of classical models. We show that behavioral changes of individuals may sensibly affect the epidemic dynamics.

Beschreibung: In this paper, we demonstrate that anti-synchronization (AS) phenomena of chaotic systems with different dimensions can coexist in the finite-time with under the effect of both unknown model uncertainty and external disturbance. Based on the finite-time stability theory and using the master-slave system AS scheme, a generalized approach for the finite-time AS is proposed that guarantee the global stability of the closed-loop for reduced order and increased order AS in the finite time. Numerical simulation results further verify the robustness and effectiveness of the proposed finite-time reduced order and increased order AS schemes.

Beschreibung: Given a 2N -dimensional Cayley-Dickson algebra, where 3 ≤ N ≤ 6 , we first observe that the multiplication table of its imaginary units ea , 1 ≤ a ≤ 2N - 1 , is encoded in the properties of the projective space PG(N - 1,2) if these imaginary units are regarded as points and distinguished triads of them {ea, eb , ec} , 1 ≤ a 〈 b 〈 c ≤ 2N - 1 and eaeb = ±ec , as lines. This projective space is seen to feature two distinct kinds of lines according as a + b = c or a + b ≠ c . Consequently, it also exhibits (at least two) different types of points in dependence on how many lines of either kind pass through each of them. In order to account for such partition of the PG(N - 1,2) , the concept of Veldkamp space of a finite point-line incidence structure is employed. The corresponding point-line incidence structure is found to be a specific binomial configuration CN; in particular, C3 (octonions) is isomorphic to the Pasch (62, 43) -configuration, C4 (sedenions) is the famous Desargues (103) -configuration, C5 (32-nions) coincides with the Cayley-Salmon (154, 203) -configuration found in the well-known Pascal mystic hexagram and C6 (64-nions) is identical with a particular (215, 353) -configuration that can be viewed as four triangles in perspective from a line where the points of perspectivity of six pairs of them form a Pasch configuration. Finally, a brief examination of the structure of generic CN leads to a conjecture that CN is isomorphic to a combinatorial Grassmannian of type G2(N + 1).

Beschreibung: A differential game is formulated in order to model the interaction between the immune system and the HIV virus. One player is represented by the immune system of a patient subject to a therapeutic treatment and the other player is the HIV virus. The aim of our study is to determine the optimal therapy that allows to prevent viral replication inside the body, so as to reduce the damage caused to the immune system, and allow greater survival and quality of life. We propose a model that considers all the most common classes of antiretroviral drugs taking into account different immune cells dynamics. We validate the model with numerical simulations, and determine optimal structured treatment interruption (STI) schedules for medications.

Beschreibung: An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R+ by using extension principles. We first show that under some mild conditions, the periodization of any wavelet frame constructed by the unitary extension principle is still a periodic wavelet frame on R + . Then, we construct a pair of dual periodic wavelet frames generated by the Walsh polynomials on R + using the machinery of the mixed extension principle and Walsh–Fourier transforms.

Beschreibung: In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields Q p (for primes p), and free probability on the subalgebra Φ, generated by the Euler totient function ϕ, of the arithmetic algebra A , consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of W * -dynamical systems induced by Q p under free-probabilistic (and hence, spectral-theoretic) techniques.

Beschreibung: We investigate various scenarios for ending the San Francisco MSM (men having sex with men) HIV/AIDS epidemic (1978–1984). We use our previously developed model and explore changes due to prevention strategies such as testing, treatment and reduction of the number of contacts. Here we consider a “what-if” scenario, by comparing different treatment strategies, to determine which factor has the greatest impact on reducing the HIV/AIDS epidemic. The factor determining the future of the epidemic is the reproduction number R0; if R0 〈 1, the epidemic is stopped. We show that treatment significantly reduces the total number of infected people. We also investigate the effect a reduction in the number of contacts after seven years, when the HIV/AIDS threat became known, would have had in the population. Both reduction of contacts and treatment alone, however, would not have been enough to bring R0 below one; but when combined, we show that the effective R0 becomes less than one, and therefore the epidemic would have been eradicated.

Beschreibung: In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag–Leffler function, including, for example, certain basic properties, Laplace transform, Mellin transform and Euler-Beta transform. Further, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag–Leffler function are investigated. Some interesting special cases of our main results are also pointed out.