Farhad Jafari

University of Wyoming/University of Minnesota · Mathematics (WY)/Radiology (MN)

The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

The ability to asymptotically stabilize control systems through the use of continuous feedbacks is an important topic of control theory and applications. In this paper, we provide a complete characterization of continuous feedback stabilizability using a new approach that does not involve control Lyapunov functions. To do so, we first develop a sli...

Local asymptotic stabilizability is a topic of great theoretical interest and practical importance. Broadly, if a system \(\dot {x} = f(x,u)\) is locally asymptotically stabilizable, we are guaranteed a feedback controller u(x) that forces convergence to an equilibrium for trajectories initialized sufficiently close to it. A necessary condition was...

Feedback asymptotic stabilization of nonlinear control systems is an important topic of control theory and applications. Broadly speaking, if the system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, then there exists a feedback control $u(x)$ ensuring the convergence to an equilibrium for any trajectory starting from a point sufficient...

Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We establish a modified Radon transform (MRT) via convolution with a mollifier and obtain its inversion formula....

Local asymptotic stabilizability is a topic of great theoretical interest and practical importance. Broadly, if a system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, we are guaranteed a feedback controller $u(x)$ that forces convergence to an equilibrium for trajectories initialized sufficiently close to it. A necessary condition was...

Moment methods to reconstruct images from their Radon transforms are natural, can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We establish a modified Radon transform (MRT) via convolution with a mollifier and obtain its inversion formula. The relationship of t...

It is well known from the seminal Brockett's theorem that the openness property of the mapping on the right-hand side of a given nonlinear ODE control system is a necessary condition for the existence of locally asymptotically stabilizing continuous stationary feedback laws. However, this condition fails to be sufficient for such a feedback stabili...

Putinar and Vasilescu (1999) have given an algebraic characterization of Hamburger moment sequences in several variables. In this paper we study some sparse moment subsequences of Hamburger moment sequences and consider the problem of completion of these moment subsequences.

Background: Proliferation and expansion of security risks necessitates new measures to ensure authenticity and validation of GMOs. Watermarking and other cryptographic methods are available which conceal and recover the original signature, but in the process reveal the authentication information. In many scenarios watermarking and standard cryptog...

The standard (nonlinear) problem of optimal control or variational calculus can be converted into a (linear) problem over the space of measures. Function theoretic considerations of the variational problem fur- ther reduces this problem to a problem of moments with respect to specific classes of (orthogonal) polynomials. While semidefinite programm...

Partial sequences and subsequences of Hamburger moment sequences arise where data have been lost or interpolation is sought. All the relevant questions dealing with full moment sequences, such as positivity and partial positivity, relationship between the corresponding measures and determinacy can be posed for the partial data. In this paper, we ch...

While several aspects of the classical problem of moments still stand unsolved, recent considerations of its sparse cases have taken the moment problem to the next level. In this paper, we describe a class of sparse moment multisequences. A subsequence of a moment sequence is not necessarily a moment sequence. We identify a class of subsequences of...

It is well known that the cornerstone of quantum mechanics is the famous Heisenberg uncertainty principle. This principle, which states that the product of the uncertainties in position and momentum must be greater than or equal to a very small number proportional to Planck’s constant, is typically taught in quantum mechanics courses as a consequen...

The Radon transform is one of the most powerful tools for reconstructing data from a series of projections. Reconstruction of Radon transform with missing data can be closely related to reconstruction of a function from moment sequences with missing terms. A new range theorem is established for the Radon transform $Rf$ on $L^1$ based on the Hamburg...

In this paper we give solutions to Hamburger moment problems with missing entries. The problem of completing partial positive sequences is considered. The main result is a characterization of positive definite completable patterns, namely patterns that guarantee the existence of Hamburger moment completion of a partial positive definite sequence. M...

DNA storage of information is emerging as the next-generation approach to archiving vast amounts of data. Various sophisticated approaches for data storage in DNA have been proposed. Herein we present a multistep algorithm designed to detect and/or correct errors introduced at any stage of the DNA storage process, including those during message DNA...

This paper proposes an approximation method to achieve optimum possible values of Spearman’s rho for a special class of copulas.

A proposal is given for a possible understanding of the unusual spin correlation that is found between two separated spin one-half particles, which originally formed a two-particle spin zero singlet quantum mechanical pair state. As the Bell inequality has shown that it is not possible to understand such spin correlations using a precise hidden var...

We give two characterizations of cones over ellipsoids in real normed vector spaces. Let $C$ be a closed convex cone with nonempty interior such that $C$ has a bounded section of codimension $1$. We show that $C$ is a cone over an ellipsoid if and only if every bounded section of $C$ has a center of symmetry. We also show that $C$ is a cone over an...

We provide a new proof for the description of holomorphic and biholomorphic flows on multiply connected domains in the complex plane. In contrast to the original proof of Heins (1941) we do this by the means of operator theory and by utilizing the techniques of universal coverings of the underlying domains of holomorphic flows and their liftings on...

This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spearman's rho and Kendall's tau f...

The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on infinite sequences of real numbers to be moment sequences. Further, works by Carath\'{e}odory, Schur and Nevanlinna connect moment problems to problems in function theory and functions belonging to various spaces. In many problems associated with realization of a...

In this paper the strongly continuous semigroups of bounded cocycle-weighted composition operators for holomorphic flows on Hardy spaces are characterized. In the process, an easy-to-check criterion for an operator to be a weighted composition operator is established. KeywordsHolomorphic flows–Cocycles–Coboundaries–Weighted composition operators–H...

For network-on-chip (NoC) designs, optimizing buffers is an essential task since buffers are a major source of cost and power consumption. This paper proposes flow regulation and has defined a regulation spectrum as a means for system-on-chip architects to control delay and backlog bounds. The regulation is performed per flow for its peak rate and...

This paper is dealing with single phase PWM rectifier parameter optimization. A control loop has been designed to attain a suitable output DC voltage with minimum ripple, input current with minimum harmonic and maximum input power factor. In this paper these parameters have been optimized by using Genetic algorithm. To verify the effectiveness of p...

The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with affine maps. After some motivation demonstrating the importance of characterization of range spaces of bandlim...

We consider two flow control schemes for best effort traffic in on-chip architectures, which can be deemed as the solutions to the boundary extremes of a class of utility maximization problem. At one extreme, we consider the so-called rate-sum flow control scheme, which aims at improving the performance of the underlying system by roughly maximizin...

Network on chip (NoC) has been proposed as an attractive alternative to traditional dedicated busses in order to achieve modularity and high performance in the future system-on-chip (SoC) designs. Recently, end to end flow control has gained popularity in the design process of network-on-chip based SoCs. Where flow control is employed, fairness iss...

For any robotic system, fault tolerance is a desirable property. This paper uses a comparative approach to investigate fault tolerance and the associated problem of reduced manipulability of robots. It is shown that for a certain class of manipulators, the mean squared relative manipulability over all possible cases of a given number of actuator fa...

6.1 Conclusions This work proves that for a certain class of parallel manipulators functioning about a single point in its workspace, the mean squared relative manipulability over all possible cases of a given number of actuator failures is always constant irrespective of the geometry of the manipulator. In this context, optimal fault tolerant mani...

Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of ℂ n , in particular the unit ball, remain mysterious. In particular, in spite of efforts spread over quite a few decades, no characterization of the extremal rays in the cone o...

This paper extends a widely used theorem of Himmelberg to topological vector spaces whose completion have a separating dual.

This paper proposes a trajectory tracking scheme which belongs to the sliding mode control (SMC) for the 4-degree-of-freedom (DOF) parallel robots. Two fuzzy logic systems (FLS) are first put forward to replace the constant switching control gain and the width of the boundary layer. The fuzzy adaptive supervisory controller (FASC) is combined with...

This paper develops new, analytical methods to find a large class of orthogonal Gough-Stewart platforms (OGSPs) having desired properties at their home position. In contrast, prior methods have been computationally intensive, relying on numerical search techniques. By exploiting symmetry, 27 equations are reduced to only two. The new techniques are...

For any manipulator, fault tolerance is a desirable property. This paper shows that for any serial or parallel manipulator functioning about a single point in its workspace, the mean square of the relative manipulabilities over all possible failures, with a given number of links failing at a time, is always constant irrespective of the geometry of...

Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the...

A new design method for optimizing Gough-Stewart platform geometries is proposed in this paper. The prior studies are extended through optimizing both the kinematics and dynamics. Firstly, a new class of weighted orthogonal Gough-Stewart platforms (w-OGSPs) is proposed. Then the concept of simultaneously diagonal OGSPs (sd-OGSPs) is defined. The sd...

In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the...

This paper develops methods for generating classes of orthogonal Gough-Stewart platforms (OGSPs). First, a new, two-parameter class of six-strut OGSPs which leads to isotropic manipulators are found. Next, this class is extended to include redundant Gough-Stewart platforms (GSPs). For an even number of struts, the same algorithm used to generate th...

In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the...

Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the...

This paper develops new, analytical methods to find a large class of Orthogonal Gough-Stewart Platforms (OGSPs) having desired manipulabilities at a single point. In contrast, prior methods have been computationally intensive, relying on numerical search techniques. The new techniques are directly applicable to clean sheet design of micro-manipulat...

We characterize the set of all transfer matrices associated with orthogonal Gough-Stewart platforms and give estimates of the system gain for these alternative geometries. This result establishes the function space of the admissible matrices over RH^∞ where the control and design are optimized.

Optimal geometric design is of key importance to the performance of a manipulator. First, this paper extends the work in Y. Yi, et al., (2004) to generate a class of isotropic Gough-Stewart platforms (GSPs) with an odd number of struts. Then, it develops methods for finding a highly fault tolerant GSP from that class. Two optimization criteria are...

This paper develops methods for generating classes of orthogonal Gough-Stewart platforms (OGSPs). First, a new, two-parameter class of six-strut OGSPs is found. For an even number of struts, the same essential concepts used to generate the six-strut case can be employed to generate OGSPs with eight struts, ten struts, etc. Next, by exploiting invar...

Development of methods to design optimal Gough-Stewart platform geometries capable of meeting desired specifications is of high interest. Computationally intensive methods have been used to treat this problem in various settings. This paper uses analytic methods to characterize all orthogonal Gough-Stewart platforms (OGSPs) and to study their prope...

The article presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty together with related classroom activities. Clinical medical practice and theoretical and empirical literature in mathematics education and radiology were reviewed to develop and pilot model integrative classroom topics and activ...

Stabilized platforms are required for two needs: (1) isolating vibrating machinery from a precision bus, and (2) quieting and precisely pointing a payload attached to a noisy, coarsely pointed bus. The early technology was based on platforms with simple passive struts, distributed in some geometry between the bus and the payload. Passive isolators...

this article, we show that for holomorphic transformations of C , there is a strong converse: it is sufficient to consider the transformation of one straight line. More precisely, if f : C ! C is an entire function such that f(z) can take a value on a given straight line L 2 only when z belongs to a certain other straight line

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α<1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.

The computation of the norm of composition operators on Hardy spaces is very hard, even for choice of fairly simple symbol maps. In this pa- per, we shall give an approach comparing the norm of these operators with the spectral radius, the action of the operators and their adjoints on the re- producing kernel functions. Our goal is to characterize,...

We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces.

We establish the existence of regular Hermite interpolations in an arbitrary connected open subset S of a topological vector space E: given N points x(\0), ..., x(N0) in S and given directions x(ki) is an element of E for all k is an element of {1, ..., N}, i is an element of {1, ..., m} such that x(kl) not equal 0, we prove that there exists an E-...

A fundamental description of continuum mixtures is presented. The mixture is decomposed into Borel sets associated with each constituent and the mixture is defined as the union of these sets. The decomposition is initiated in Euclidean one-space, motivated by the fact that the deformation of a continuum is ultimately described by the deformation of...

This research investigates the capability of a multiprocessor system in guaranteeing the execution of critical tasks and determines the cause of deadline failures. By implementing a real-time application using an INMOS transputer and Occam language, we were able to distribute required tasks among the processors and determine their CPUs usage. We ev...

We present a new variant of the simultaneous Stone-Weierstrass approximation of a function and its partial derivatives, when the function takes its values in a Banach space, and provide an explicit and direct computation of this approximation. In the particular case of approximation by means of polynomials, we show that the simultaneous approximati...

We investigate the validity of applying a lemma of Springer to the evaluation of the H-function inversion integral. We provide examples to show that this lemma is incorrect as stated, prove several valid versions of this lemma, and investigate the use of this lemma in the context of the H-function integrals. We also investigate a question related t...

It is well known that the set of all square invertible real matrices has two connected components. The set of all m × n m \times n rectangular real matrices of rank r r has only one connected component when m ≠ n m \ne n or r > m = n r > m = n . We show that all these connected components are connected by analytic regular arcs. We apply this result...

The importance of theorems on Carleson measures has been well recognized [3]. In ]1] Chang has given a characterization of the bounded measures on L(p)(T(n)) using what one may characterize as the bounded identity operators from Hardy spaces of polydiscs in L(p) spaces. In [4] Hastings gives a similar result for (unweghted) Bergman spaces of polydi...

Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of C ⁿ . Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study compositi...

Predictive thermometry, utilizing minimally invasive sampling techniques, is an essential ingredient in the development of hyperthermia treatment planning capabilities. The authors demonstrate a powerful, but simple approach toward predicting temperature distributions in tissues, based on analytic solution, using in cylindrical symmetry, of the hea...

A method for predicting relative temperature distributions in acoustically homogeneous regions heated by acoustic sources is presented. A generalized approach is presented in which thermal distortions, produced by variable conduction and/or perfusion cooling, are approximated as an effective conductivity term in a heat-diffusion equation. Calculate...

The primary goal of this project has been to characterize the lung tissue in its in vivo ultrasonic backscattering properties in normal human subjects, and study the changes in the lung echo characteristics under various pathological conditions. Such a characterization procedure is used to estimate the potential of ultrasound for providing useful d...

It has been discovered that three theoretically derived plots of acoustic scattering for rigid immovable spheres appearing in two standard reference works are only qualitatively correct and therefore could be misleading. The reason for the inaccuracy is shown to be premature truncation of the infinite series resulting from the theory. Quantitative...

Thermal distributions of 434 MHz Erbotherm H 69 hyperthermia/diathermy generators in tissue-equivalent medium have been investigated. Thermocouples were used to measure temperatures at a set of grid points. Cylindrical and abdominal phantoms were heated and sectioned after heating to measure the temperatures at depth. Results indicate that there is...

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