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The possibility of the existence of superdiamagnetism in non-superconducting substances is discussed. Such superdiamagnetic substances may have susceptibility χ ∼− (10−3-10−2) comparable with the ideal one χ id = − 1 4 π , whereas in ordinary diamagnetic materials |χ| ⩽ 10−4 ⪡|χidz.sfnc;. It is poined out that under equilibrium superdiamagnetism may occur in toroidal type substances, for which the order parameter T is a toroidal moment density. Toroidal moment is a polar vector which changes sign under time inversion. On a microscopic level toroidal current states arise in the model of excitonic insulator with an imaginary singlet order parameter. Conditions have been found under which superdiamagnetism can be expected in such systems. Anomalous susceptibility, which is probably observed in CuCl and CdS, is possibly of superdiamagnetic nature.

The number of independent constants in the Fourier expansion of the matrix of the Hamiltonian of crystals can be diminished if the orthogonality of the states corresponding to different complex bands of the crystal is used in addition to taking account of the spatial symmetry, the symmetry relative to time inversion, and the fact that the matrix is Hermitian. Bands with the space group O7 (Si, Ge, cubic SiO2) are examined as an illustration.

Previous statements concerning the reduction of possible parity and time reversal choices for electromagnetic quantities are amplified for the sake of clearer understanding.

Conventional (point) symmetry, antisymmetry, magnetic and complete symmetry are used for the description of specific features of space, time and some crystallographic phenomena. The Onsager principle is extended to phenomena described by second-rank axial tensors. As a result it is seen that the symmetric part of such a tensor changes the sign on time reversal. The actions of two operations - time reversal R and time inversion T (T = \bar 1, 'spatial inversion') - are compared. It is shown that the equations of crystal physics derived by Voigt are in agreement with the Onsager principle.

In this paper magnetic space groups are defined. Their irreducible representations are given in terms of the irreducible representations of the group of the k-vector. The irreducible representations of the double groups and time inversion symmetry are discussed. In der vorliegenden Arbeit werden magnetische Raumgruppen definiert. Ihre irreduziblen Darstellungen werden aus den irreduziblen Darstellungen der Gruppe des k-Vektors hergeleitet. Die Darstellungen der Doppelgruppen und die Zeitumkehrsymmetrie werden diskutiert.

The quasistochastic invariance of field equations with respect to the halfgroup of relativistic endomorphisms is discussed. Tensor and spinor representations of the quasistochastic halfgroup of relativistic endomorphisms (QHRE) are obtained, and the properties of the generators of these representations are discussed in infinitesimal terms. It is shown that the generators of the corresponding types of Lorentz-group representations are contained in these generators. The form of the spinor-tensor coupling in the QHRE is the same as in the Lorentz group, although the content is different since the QHRE is constructed with an account of Wigner time inversion.

Two derivations of Onsager's reciprocal relations are presented in simplified form, and the range of their validity is discussed.

Group-theory methods are used to study the dispersion laws near symmetric points of the Brillouin zone for body-centered rhombic crystals with an account of time inversion and the spin-orbit interaction. The effects of changes in the lattice constant on the qualitative features of the energy spectrum are discussed.

After a brief discussion of space inversion and time inversion, the distinction between magnetic and nonmagnetic crystal classes is illustrated by reference to cubic lattices. The appearance of “forbidden” effects in various crystal classes is discussed and recent experimental work on pyromagnetism, the magnetoelectric effect and piezomagnetism in antiferromagnetic materials is reviewed.

A relation is derived between unitary transformations in the impact parameter approximation or in the classical path method. The unitary transformations describe the behaviour of the electrons before and after the trajectory, which is followed by heavy particles, crosses the turning point. The properties used to establish the relation are the assumption that the trajectory of heavy particles is determined by a spherically symmetric potential as well as the invariance of the Hamiltonian under rotation and the time inversion invariance. To facilitate the use of this relation an additional relation is derived using the fact that a trajectory determined by a spherically symmetric potential is constrained to a plane.

The paradoxical aspects of the quantum-mechanical measuring process continue to provoke numerous discussions, inducating a growing interest in the basic problems of quantum mechanics (1,2). The purpose of the present note is to clarify our views on this important problem and to contras them with the views expressed in some recent publications on the same subject (1h,i).

Purpose To assess the diagnostic effectiveness of unenhanced-multiparametric magnetic resonance imaging (mp MRI) as an alternative to gadolinium (Gad)-enhanced MRI in the characterization of vertebral marrow infiltrative lesions. Patients and methods A prospective evaluation of fifty-six patients with suspected or untreated vertebral metastases undergoing MRI of the spine at 1.5 T was carried out. Two groups of sequences were assigned and compared for the characterization of marrow infiltrative lesions: group [A] unenhanced-mp MRI (including T1-weighted, T2-weighted, short time inversion recovery (STIR), diffusion weighted imaging (DWI) and in/opposed phase sequences) and group [B] gadolinium-enhanced MRI (including T1-weighted, T2-weighted, STIR and T1-weighted fat-suppressed gadolinium-enhanced sequence). Qualitative and quantitative image analysis was performed and compared. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and accuracy for both imaging techniques were calculated. Results There was no statistical significant difference between unenhanced-multiparametric MRI and gadolinium-enhanced MRI as regards their diagnostic performance in differentiating benign from malignant vertebral marrow infiltrative lesions ( p > 0.05) with calculated sensitivity (94% vs. 97%), specificity (92% vs. 88%), positive predictive value (94% vs. 91%), negative predictive value (92% vs. 95%) and (93% vs. 93%) accuracy. Conclusion Unenhanced-multiparametric MRI is compatible with gadolinium-enhanced MRI in reliable characterization of marrow infiltrative lesions. The routine MRI protocol of cancer patients should be altered to accommodate the evolving MRI technology and cost effectively substitute the need for a gadolinium enhanced scan.

Let $X_1, X_2,\cdots$ be i.i.d. random variables with mean 0 and variance 1. Let $S_n = X_1 + \cdots + X_n$, and let $\{H_n\}$ be the standard partial sum processes on $\lbrack 0, \infty)$ defined in terms of the $S_n$'s and normalized as in Strassen. Each function of the "tail" behavior of the process $H_n$ is the dual of a function of the "initial" behavior of the process $H_n$, the duality being induced by the time inversion map $R$. The dual role of "initial" and "tail" functions is used to exploit an extension of Strassen's invariance theorem for the law of the iterated logarithm due to Wichura, and thereby obtain limit theorems for a variety of functions of the "tail" behavior of the sums $S_n$. For example, with probability one, $$\lim \sup_{n\rightarrow \infty} (n/2 \log \log n)^\frac{1}{2} \max_{n\leqq k < \infty} (k^{-1}S_k) = 1$$ and $$\lim \sup_{n\rightarrow \infty} n^{-1} \max \{k \geqq 1: k^{-1}S_k \geqq \theta(2 \log \log n/n)^\frac{1}{2}\} = \theta^{-2}.$$

Recently Groeneboom [1] studied the concave majorant process of a Brownian motion (Bt, t ≤ O). The purpose of this note is to take a fresh look at some of Groeneboom’s results in the context of path decompositions of Williams [7], and to give a simple new description of this concave majorant process.

To modelize a nonstationary random phenomenon, it is tempting to write Yn = f(n) + Xn where X is stationary and the trend f(n) is a deterministic function to be adequately selected; f(n) is often assumed to be the sum of a polynomial in n and of linear combinations of cos nλj and sin nλj,= 1,2, ..., K. A first approach is to estimate separately f (for instance by least squares methods (cf. [15]) and the covariance structure of X.

In the recent past philosophers have looked at reductions of various species of scientific theories in general and microreductions in particular, using elementary semantics and set-theoretical tools (see, e.g. Bunge (1970), Causey (1972), Stegm?ller (1976), and Spector (1978)). In this paper I wish to look at the reduction of macrotheories to micro theories with special regards to invariance under time inversion or simply irr ever sibility. My interest in microreduction is stimulated by the fact that the traditional methods employing syntactic and/or semantic interpre? tations of reduced theories within reducing theories do not seem to apply to irreversible reductions. A third, mediating theory is needed, which is 'probabilistic' rather than 'deterministic' in nature. Worse, the probabilis? tic theory is essentially macroscopic in the sense that its assumptions (such as Markovianness and Maximum Entropy) are tested macroscopically. Consequently, the reduction is only relative, relativized by the reference (macroscopic probabilistic) theory. Also, the relativizing theory may be chosen somewhat independently of the underlying microtheory. Somewhat naively it would seem that an explanatory passage from a microtheory T to a macrotheory T' is still a version if not deductive then inductive of semantic interpretation, mediated by a probabilistic theory T", as the picture shows

An adaptation of the work by Huber and Muller (see Electronic Letters, vol.33, no.5, p.368-69, 1997) on partial transmit sequences (PTS) for the reduction of the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) is described.

Identification of the time inversion operator θ with the magnetic moment inversion operator A in finding the symmetry restrictions on the form of transport tensors in solids is shown to be incorrect.

Points of agreement and disagreement with Post's remarks on the author's discussion of the criteria to be used for reducing the eight parity and time reversal symmetry choices that the formally possible for electromagnetic quantities are noted.

Wave propagation in a vertically inhomogeneous ocean exhibits effective dispersion although the medium itself is nondispersive. Wave dispersion is weak at sufficiently high frequencies. The resulting local plane wave spectral representation of a source‐excited sound field may then be inverted exactly to yield the impulsive response. Alternative inversion techniques are the Cagniard‐DeHoop and the more general Chapman procedures. Both have limitations which are overcome by an analytic function approach, from which either a generalized Cagniard‐DeHoop or the Chapman formulations are derived systematically by manipulations in the complex spectral plane. The three methods are compared and illustrated on caustic‐forming multiple reflected ray fields and on refraction arrivals.