On states, on a lattice, with half-integral charge

In certain molecular models, and related one-dimensional field theories, localized objects appear with half-integral expectation values of charge. We consider whether these states are eigenstates of charge, with half-integral eigenvalue. We find that it is indeed so for a suitably diffuse definition of the charge operator in question. This diffuse charge operator has a spectrum which approaches a continuum. The analysis is made on a lattice, to avoid divergence ambiguities, and on a finite length, which is only subsequently made large. The half-integral charge phenomenon is not tied to solitons, but can also arise as an end effect.

Quaternary unary operators

Unary operators are functions of a single variable. Realization of quaternary unary operators (QUOs) using quaternary multiplexer (QMUX) is presented in this paper. QUOs are divided into eight groups on the basis of the number of change overs in the output for an input sequence of 0, 1, 2, 3. This grouping reduces the hardware required to realize them. QMUX with two, three, and four input lines are proposed for the realization of QUOs belonging to the eight groups. A systematic procedure for the selection of QMUX and the implementation of the QUOs are given. The QMUXs are designed using CMOS ICs. The hardware required for their implementation is also discussed.

Evolution in design of integral leg prosthesis leads to improved outcomes

Developments of surgical attachments for bone-anchored prostheses are slowly but surely winning over the initial disbelief in the orthopedic community. Clearly, this option is becoming accessible to a wide range of individuals with limb loss. Seminal studies have demonstrated that the pioneering procedure relying on screw-type fixation engenders major clinical benefits and acceptable safety. The surgical procedure for press-fit implants, such as the Integral-Leg-Prosthesis (ILP) has been described Dr Aschoff and his team. Some clinical benefits of press-fit implants have been also established. Here, his team is once again taking a leading role by sharing the progression over 15 years of the rate of deep infections for 69 individuals with transfemoral amputation fitted with three successive refined versions of the ILP. By definition, a double-blind randomized clinical trial to test the effect of different fixation’s design is difficult. Alternatively, Juhnke and colleagues are reporting the outcomes of action-research study for a cohort of participants. The first and foremost important outcome of this study is the confirmation that the current design of the IPL and rehabilitation program are altogether leading to an acceptable rate of deep infection and other adverse events (e.g., structural failure of implant, periprosthetic factures). This study is also providing a strong insight onto the effect of major phases in redesign of an implant on the risk of infection. This is an important reminder that the development of a successful osseointegrated implant is unlikely to be immediate but the results of a learning curve made of empirical and sequential changes led by a reflective clinical practice. Clearly, this study provided better understanding of the safety of the ILP surgical and rehabilitation procedure while establishing standards and benchmark data for future studies focusing on design and infection of press-fit implants. Complementary observations of relationship between infection and cofounders such as loading of the prosthesis and prosthetic components used would be beneficial.Further definitive evidences of the clinical benefits with the latest design would be valuable, although an increase in health related quality of life and functional outcomes are likely to be confirmed. Altogether, the authors are providing compelling evidence that bone-anchored attachments particularly those relying on press-fit implants are an established alternative to socket prostheses.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Tuning of PID controllers for water networks—different approaches

Better operational control of water networks can help reduce leakage, maintain pressure, and control flow. Proportional integral derivative (PID) controllers, with proper fine-tuning, can help water utility operators achieve targets faster without creating undue transients. The authors compared three tuning methods, in different test situations, involving flow and level control to different reservoirs. Although target values were reached with all three tuning methods, the methods’ performances varied significantly. The lowest performer among the three was the method most widely used in the industry—standard tuning by the Ziegler-Nichols method. Achieving better results was offline tuning by genetic algorithms. Achieving the best control, though, was a fuzzy logic–based online tuning approach—the FZPID controller. The FZPID controller had fewer overshoots and took significantly less time to tune the gains for each problem. This new tuning approach for PID controllers can be applied to a variety of problems and can increase the performance of water networks of any size and structure

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

On solitons with half integral charge

Can certain soliton states, with half integral expectation value of charge, be also eigenstates of charge X with half integral eigenvalue? It can be so only with a somewhat sophisticated definition of charge.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

On the Solution of Certain Simultaneous Pairs of Dual Integral Equations

Mit einer direkten Methode, bei der der Erdelyi-Kober- und der modifizierte Hankel-Operator Anwendung finden, werden gewisse Systeme aus zwei bzw. drei Paaren dualer Integralgleichungen mit Bessel-Kernen in geschlossener Form gelöst. Für bestimmte Funktionenklassen und Ordnungen der Bessel-Funktionen ist die Vorgehensweise angebrachter und geeigneter als die bereits existierenden Methoden.

Determination of integral fringe order in photoelasticity

The paper describes a method to determine the integral fringe order associated with a fractional fringe value that is measured using Tardy or other similar compensators. The method makes use of two different wavelengths of light to determine the fractional fringe values. Further, it does not assume the independence of the material fringe constant on the wavelength of light used. From these measured fractional fringe values, the associated integral fringe order is determined. A method to construct a ready-reckoner table is also described which helps to identify the integral fringe order from any two measured fractional fringe values.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.