SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM

The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. In this paper, we accomplished the concept of Hankel convolution and continuous Bessel wavelet transform to solve certain types of integral equations (Volterra integral equation of first kind, Volterra integral equation of second kind and Abel integral equation). Also distributional wavelet transform and generalized convolution will be applied to find the solution of certain Integral equations.

The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

We characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjugations by Zak transforms.

Perubahan Struktur Organisasi Kepanitiaan dalam Festival Film Mahasiswa UCIFEST

Festival film berkontribusi besar dalam menyelesaikan masalah distribusi bagi film-film alternatif seperti film-film karya mahasiswa yang ada di Indonesia. Film –film mahasiswa yang tidak dapat masuk ke jalur komersil, membutuhkan ruang atau etalase untuk menunjukkan karya mereka. Kebutuhan akan memiliki ruang eksebisi dan distribusi bagi film-film alternatif, menjadi faktor terbentuknya festival-festival film kampus. Sebagai festival film yang berada dibawah institusi dan dibentuk dengan semangat independen dari mahasiswa, festival film dapat bertahan dalam berbagai kondisi. Jaringan yang diciptakan oleh mahasiswa antar universitas juga menjadi kekuatan berlangsungnya festival film. Struktur organisasi kepanitiaan dibuat menyesuaikan kebutuhan festival film. Struktur organisasi yang dibentuk harus berjalan secara efektif dan efisien demi tercapainya kesuksesan festival film. Changes in the Organizational Structure of the Committee in the UCIFEST Student Film Festival Abstract: Film festivals contribute to solving distribution for alternative films. A short film created by students cannot enter the commercial path or screen in the movie theatre. The need to have exhibition and distribution spaces for the alternative film is a factor that the students make short film festivals on the campus. As a film festival under the university or institution, a film festival can survive in various conditions. This is because of the festival formed with the spirit of independence by students. Besides that, the network created by students between the communities or universities is also the strength of the short film festival. Another essential factor for the film festival is the organizational structure. The organizational structure must run effectively and efficiently to achieve the success of the film festival.

Algebraic and differential properties of polynomial Fourier transformation

Methods of integral transformations of (generalized) functions are widely used in the solution of initial and boundary value problems for partial differential equations. However, many problems in applied mathematics require a nonlinear generalization of distribution spaces. Besides, an algebraic structure of a space of distributions is desirable, which is needed, for example, in quantum field theory.In the article, we use the adjoint operator method as well as technique of symmetric tensor products to extended the Fourier transformation onto the spaces of so-called polynomial rapidly decreasing test functions and polynomial tempered distributions. In such spaces it is possible to solve some Cauchy problems, for example, infinite dimensional heat equation associated with the Gross Laplacian.Algebraic and differential properties of the polynomial Fourier transformation are investigated. We prove some analogical to classical properties of this map. Unlike to the classic case, the spaces of polynomial test and generalized functions have algebraic structure. We prove that polynomial Fourier transformation acts as homomorphism of appropriate algebras. It is clear that the classical analogue of such property is absent.

Multiplication of Distributions and Algebras of Mnemofunctions

In this paper, we discuss methods and approaches for definition of multiplication of distributions, which is not defined in general in the classical theory. We show that this problem is related to the fact that the operator of multiplication by a smooth function is nonclosable in the space of distributions. We give the general method of construction of new objects called new distributions, or mnemofunctions, that preserve essential properties of usual distributions and produce algebras as well. We describe various methods of embedding of distribution spaces into algebras of mnemofunctions. All ideas and considerations are illustrated by the simplest example of the distribution space on a circle. Some effects arising in study of equations with distributions as coefficients are demonstrated by example of a linear first-order differential equation.

Steering Options for Maneuvering a Particle on a Surface

We consider the general problem of steering an infinitesimal propelled and steerable particle with no rotational inertia traversing on a mathematically smooth (vs. frictionless) surface, where both the speed and body yaw rate serve as inputs to the system and lateral motion is not allowed, i.e. through a no sideslip condition. More specifically, focus is on derivation of relevant state equations in control input form, numerical and visual confirmation of state equation accuracy through specific simulations, and exploring interesting approaches to nonholonomic path planning with associated numerical simulation and visualization. Given the state equations (3rd order), in the interests of practical validation, they were exercised by considering motion on a number of smooth surfaces. The surfaces were selected for a variety of reasons, such as: the resulting qualitative trajectory is known a priori, there exists an opportunity to check numerical results with respect to previous results, or the surfaces are iconic and/or are geometrically rich. Nonholonomic steering on the surface is a very interesting and challenging problem and several approaches are investigated: (1) steering using sinusoids (detailed), (2) steering on a trajectory, and (3) “drive-and-turn” (valid in this case). Prior to implementing the steering using sinusoids algorithm, it was necessary to transform the system into “one-chained” form. The first step entailed conversion to an approximate one-chained form model that possesses a certain structure, from which the process established by Murray and Sastry can be successfully launched, where two special smooth scalar functions of the states are sought that possess special relationships to Lie-related distribution spaces associated with the control input vectors. Inputs are then transformed as well via specialized Lie derivatives. It was demonstrated through simulation that steering to an arbitrary system state on a faceted surface can be accomplished with sinusoidal inputs in only one maneuver set (i.e. maneuver A & B). Using this fact, the work presented culminates with steering to an arbitrary system state on a smooth surface that can be accomplished by essentially iterating on a steering algorithm that assumes the particle is on a plane tangent to the smooth surface at the desired destination. In this regard, it is shown that a sequence of maneuver sets converges rather quickly in the example demonstrated. Applications of this work pertain to the fairly general situation of steering a vehicle on a smooth surface, a practical vehicle navigation and control problem.