Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

Rayleigh reciprocity relations： Applications

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation： higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green＇s function retrieval from volume noises.

Inverse Electromagnetic Scattering by a Penetrable Chiral Object

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.

Onsager principle as a tool for approximation

Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation.The principle has been shown to be useful in deriving many evolution equations in soft matter physics.Here the principle is shown to be useful in solving such equations approximately.Two examples are discussed：the diffusion dynamics and gel dynamics.Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number.In the first part of this paper,adequate preparations for the main uniqueness result are made.We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves.Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method.Finally,the a priori estimates of solutions to the general transmission problem with boundary data in L^(p)(δΩ)(1<p<2)are proven by the boundary integral equation method.In the second part of this paper,we give a novel proof on the uniqueness of the inverse conductive scattering problem.

On an Application of the Improved Maximum Product Criterion to Inverse Acoustic Scattering in a Layered Medium

In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

Comment to Guynn’s Fine-Structure Constant Approach

Sommerfeld’s fundamental fine-structure constant α once more gives reason to be amazed. This comment is a Chapter of a publication in preparation dealing mainly with golden ratio signature behind Preston Guynn’s famous matter/space approach. As a result we present a relation of α to the galactic velocity , mediated by the circle constant π, which points to an omnipresent importance of this constant and its intrinsic reciprocity pecularity: α ≈ π2|βg| respectively . The designation fine-structure constant should be replaced simply by Sommerfeld’s constant. We present golden mean-based approximations for α as well as for electron’s charge and mass and connect the word average value of interaction coupling constant αs(mz) with |βg|.

Galactic Route to the Strong Coupling Constant αs(mz) and Its Implication on the Mass Constituents of the Universe

Some fundamental physical quantities need an alternative description. We derive the word average value of interaction coupling constant αs(mz) from the observed maximum galactic rotation velocity by the simple relation , where is the velocity, at which the difference between galactic rotation velocity and Thomas precession is equal, and α is Sommerfeld’s constant. The result is in excellent agreement with the value of αs = 0.1170 ± 0.0019, recently measured and verified via QCE analysis by CERN researchers. One can formulate a reciprocity relation, connecting αs with the circle constant: . It is the merit of Preston Guynn to derive the Milky Way maximum value of the galactic rotation velocity βg, pointing to its “extremely important role in all physics”. The mass (energy) constituents of the Universe follow a golden mean hierarchy and can simply be related to the maximum of Guynn’s difference velocity respectively to αs(mz), therewith excellently confirming Bouchet’s WMAP data analysis. We conclude once more that the golden mean concept is the leading one of nature.

Abel’s lemma on summation by parts and partial q-series transformations

The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.

Reconstruction of the shape of object with near field measurements in a half-plane

We consider a mathematical problem modelling some characteristics of near field optical microscope.We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem.Some numerical examples to show the feasibility of the method are presented.