arXiv subjects

A. Gersten

Publications and source records attributed to A. Gersten.

8 recordsLinked to original sources

arXiv2005

Evaluation of the Extension of the Cerebral Blood Flow and its Main Parameters

Among the major factors controlling the cerebral blood flow (CBF) - cerebral perfusion pressure, arterial partial pressure of oxygen (PaO2), cerebral metabolism, arterial partial pressure of carbon dioxide (PaCO2), and cardiac output, the effect of PaCO2 is peculiar in being independent of autoregulatory CBF mechanisms and it allows to explore the full range of the CBF. We have developed a simple physical model, and have derived a simple four parameter formula, relating the CBF to PaCO2. The parameters can be extracted in an easy way, directly from the experimental data. With this model five experimental data sets of human, rats, baboons and dogs were well fitted. The same type of parametrization was also used successfully for fitting experimental data of PaO2 of dogs. We have also looked on the dependence of the parameters on other factors and were able to evaluate their dependence on the mean arterial blood pressure.

physics.med-ph↗

arXiv1999

Conserved Currents of the Maxwell Equations with Electric and Magnetic Sources

New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to both the field strengths and the sources. In this way, conserved currents can be found for the field strengths and the electric or magnetic sources. Furthermore, using the equations of motion, the electric or magnetic sources can be eliminated, leading to conserved currents for the field strengths only (in the presence of electric and magnetic sources). Another new feature is the construction of a Lagrangian invariant under the duality transformation for both field strengths and electric and magnetic sources. The conserved current, after the elimination of electric and magnetic sources, depends on the field strengths only. The conserved quantity is related to the total helicity of the electromagnetic field.

physics.gen-ph↗

arXiv1999

The RR interval spectrum, the ECG signal and aliasing

A reliable spectral analysis requires sampling rate at least twice as large as the frequency bound, otherwise the analysis will be unreliable and plagued with aliasing distortions. The RR samplings do not satisfy the above requirements and therefore their spectral analysis might be unreliable. In order to demonstrate the feasibility of aliasing in RR spectral analysis, we have done an experiment which have shown clearly how the aliasing was developed. In the experiments, one of us (A.G) had kept his high breathing rate constant with the aid of metronome for more than 5 minutes. The breathing rate was larger than one-half the heart rate. Very accurate results were obtained and the resulting aliasing well understood. To our best knowledge this is the first controlled experiment of this kind coducted on humans. We compared the RR spectral analysis with the spectrum of the ECG signals from which the RR intervals were extracted. In the significant for RR analysis frequencies (below one-half Hertz) significant differences were observed. In conclusion we recommend to study the spectral analysis of the ECG signal in the free of aliasing frequency range.

physics.med-ph↗

arXiv1999

Maxwell equations as the one-photon quantum equation

Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.

quant-ph↗

arXiv1999

Dirac's Representation Theory as a Framework for Signal Theory. I. Discrete Finite Signals

We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection operators is stressed. A Dirac space is defined, which is spanned by an orthonormal basis labeled with the time points. An infinite number of orthonormal bases is found which are labeled with frequencies, they are distinguished by the continuous parameter a. In a way, similar to one used in quantum mechanics, self-adjoint operators (observables) and averages (expectation values) are defined. Non orthonormal bases are discussed and it is shown, in an example, that they are less stable compared to the orthonormal ones. A variant of the sampling theorem for finite signals is derived. The aliasing phenomenon is described in the paper in terms of aliasing symmetry. Relations between different bases are derived. The uncertainty principle for finite signals is discussed.

physics.med-ph↗

arXiv1999

Dirac's Representation Theory as a Framework for Signal Theory. II. Infinite Duration and Continuous Signals

We generalize previous results and demonstrate that the Dirac representation theory can be effectively adjusted and applied to continuous or discrete signals of infinite time duration. The role of the identity and projection operators is emphasized. The sampling theorem is viewed from the point of view of orthogonal physical states. An orthogonal basis which spanned the time space, ceases to be orthogonal and becomes overcomplete if the domain of frequencies is restricted in a bandwidth. In this case there exists an infinite number of sub-bases of discrete times which are orthogonal and complete. The relation between the overcomplete bases and a complete one is the essence of the sampling theorem. The signal theory is reformulated in the framework of the Dirac bra-kets. The case of signals existing for positive time is treated in detail.

physics.med-ph↗

arXiv1999

Orthogonality and Boundary Conditions in Quantum Mechanics

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets) depend on two quantum numbers: energy and parity. With the aid of projection operators the particles are confined to a constrained region, in a way similar to the action of an infinite well potential. From the resulting overcomplete basis only the mutually orthogonal states are selected. Four solutions are found, corresponding to different non-commuting Hamiltonians. Their energy eigenstates are labeled with the main quantum number n and parity "+" or "-". The energy eigenvalues are functions of n only. The four cases correspond to different boundary conditions: (I) the wave function vanishes on the boundary, (II) the derivative of the wavefunction vanishes on the boundary,(III) periodic (symmetric) boundary conditions, (IV) periodic (antisymmetric)boundary conditions . Among the four cases, only solution (III) forms a complete basis in the sense that any function in the constrained region, can be expanded with it. By extending the boundaries of the constrained region to infinity, only solution (III) converges uniformly to the free particle states. Orthogonality seems to be a more basic requirement than boundary conditions. By using projection operators, confinement of the particle to a definite region can be achieved in a conceptually simple and unambiguous way, and physical operators can be written so that they act only in the confined region.

quant-ph↗

arXiv1999

Incomplete Delta Functions

By applying projection operators to state vectors of coordinates we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call "incomplete delta functions". We show that this class of functions satisfy identities similar to those satisfied by the Dirac delta function. The incomplete delta functions may be employed advantageously in projected subspaces and in the link between functions defined on the whole space and the projected subspace. We apply a similar procedure to finite dimensional vector spaces for which we define incomplete Kronecker deltas. Dispersion relations for the momenta are obtained and ''sums over poles'' are defined and obtained with the aid of differences of incomplete delta functions.

quant-ph↗