Formal Resemblance Research Articles

Some Trade Theorems with a Public Intermediate Good

This paper considers the implications for the Stolper-Samuelson and Rybczynski theorems of a pure public intermediate good. Necessary and sufficient conditions for the theorems to hold in their strong versions are derived. They show a close formal resemblance to those known from the model with variable returns to scale internal to industries. The dual nature of the two theorems is shown to be preserved. Lastly, sufficiency conditions for either theorem to hold are presented.

The North Carpathians at the beginning of the Migration Period

The problem of identification of the earliest Slavic settlement in central Europe drew researchers’ attention to the archaeological finds of the Late Roman and Migration periods. The simple hand-made pottery of this period in the northern Danube region showed a certain formal resemblance to the vessels of Early Slavic cultures, which provoked the idea of a direct time connection between the first wave of the Slav expansion from the east and the horizon of the preceding Germanic settlement in this territory. A find group from northeast Slovakia, known mainly from the small settlement at Presov (Chropovský 1962; Točík 1965; Chropovský & Ruttkay 1985), the ’Prešov‘ type, seemed to provide the geographical connection of this ethnic shift. However, different opinions were also expressed, pointing to a possible relationship with the Late Przeworsk culture milieu (Budinský-Krička 1963: 36–7), or connecting the genesis of the Prešov finds with the development of local settlement of the Later Roman period (Lamiová-Schmiedlová 1969: 478; Kolník 1980: 202). Investigations in the North Carpathian area has provided new evidence during the last few years enabling a first evaluation of its settlement.

An observation concerning Ryser's conjecture

An r-graph is another name for an r-uniform hypergraph. An r-graph H = (V, 8) is called r-paeandY= v(H) is the match&g number of H, i.e., the largest size of a family of pairwise disjoint edges). A well known conjecture of Ryser is that in an r-partite r-graph the stronger inequality z < (r 1)v holds. In this note we prove a result which bears at leaat formal resemblance to this conjecture. The following result appliw to all r-graphs:

Mechanisms of antioxidant action: The photo-antioxidant behaviour of nitroalkanes

Nitro tertiary alkanes are photo-antioxidants for polyolefins. The mechanism is shown to involve photolysis to NO 2 which can subsequently participate in the catalytic deactivation of photochemically formed macroalkyl radicals. The mechanism proposed bears formal resemblance to that of hindered piperidinoxyls in the antioxidant mechanism of the hindered piperidines.

Realization of the Logical Operation XOR by a Synergetic Computer

In this section I wish to show how the XOR operation (the exclusive “or”) can be performed by a dynamical system which has a close formal resemblance to a liquid forming hexagons in a nonequilibrium state. This will allow us to construct a synergetic computer for this operation. Historically, the XOR operation has played an important role in the discussion of parallel computers, or in other words, connectionist machines or neurocomputers. Following up the basic concepts of McCulloch and Pitts, Rosenblatt (1958) had developed his perceptron. The continuation of this work was “killed” (to use Sejmour Papert’s words) by the influential book by Minsky and Papert (1961), “Perceptrons”. In that book they showed that Rosenblatt’s perceptron cannot perform the XOR operation. Nowadays, the XOR operation can be performed by neurocomputers with several layers and a sigmoid activation curve (instead of the original steep threshold curve of McCulloch and Pitts).

Modified solenoid scattering for the Aharonov-Bohm effect

A method of partial-wave analysis is used to extend the treatment of Aharonov and Bohm (1959) for the scattering from an unscreened solenoid of infinitesimal radius to include screening and non-zero radius. The method yields a scattering amplitude which bears a formal resemblance to that appropriate to modified Coulomb scattering. The scattering amplitude and the momentum transfer cross section retain a dependence on the enclosed flux as the screening barrier becomes infinite, resulting in a component of force, periodic in the enclosed flux, being exerted on the barrier. The resulting implications concerning the locality of electromagnetic interactions are discussed. The force is shown to persist when the conditions of strict impenetrability are relaxed and the possibility of directly observing this quantum force is examined.

Action principle and equations of motion for nonabelian monopoles

Monopoles in gauge theories have an intrinsic interaction with the gauge field. The definition of a monopole as a topological charge implies a certain constraint coupling the gauge field to the coordinates of a particle carrying that charge. Hence, even starting with the free action, the constraint will give equations of motion in which field and particle interact. Applied to electromagnetism, this procedure gives the Maxwell and Lorentz equations. In this paper, we apply the same idea to nonabelian monopoles to deduce their equations of motion which are otherwise unknown. To surmount certain technical difficulties connected with patching, loop space techniques are developed to solve the variational problem. A closed set of equations are obtained, which are analogous to the Maxwell and Lorentz equations, and bear also a formal resemblance to the Wong equations for a “classical” point source of Yang-Mills fields.

Wetting of the container wall as a critical-point phenomenon. III. Wetting by contacting conjugate solutions of ternary systems

In the ternary systems benzene-ethanol-water and ethyl acetate-ethanol-water, the contact angles of the meniscus between two immiscible liquid phases (i.e., conjugate solutions) and a solid substrate tend toward 90° as compositions approach the consolute point at a constant temperature; just as, in a binary system, the contact angles between the corresponding three phases have been shown (in the previous paper of this series) to tend toward 90° as the temperature approaches the critical point. The quantitative expression for the variation of the contact angle with the concentration of the cosolvent in the vicinity of the consolute point in a ternary system also bears a formal mathematical resemblance to that found for the corresponding variation of the contact angle with temperature in a binary system.

Functional equations for circle homeomorphisms with golden ratio rotation number

The investigation of a scaling limit for mappings of the circle to itself with golden ratio rotation number leads to a pair of functional equations with at least a formal resemblance to the functional equation using the accumulation of period-doubling bifurcations. We discuss the general theory of these functional equations, assuming that solutions exist.

Evidence for a lipoxygenase mechanism in the biosynthesis of epoxide and dihydroxy leukotrienes from 15(S)-hydroperoxyicosatetraenoic acid by human platelets and porcine leukocytes.

Leukocyte preparations convert the hydroperoxy icosatetraenoic acids 5(S)-HPETE and 15(S)-HPETE to the unstable leukotriene epoxides LTA4 and 14,15-LTA4. In several ways, the conversion of 5- or 15-HPETE to leukotriene epoxide bears a formal mechanistic resemblance to the reaction catalyzed by the 12-lipoxygenase in the conversion of arachidonic acid to 12(S)-HPETE. Points of similarity include enzymatic removal of a hydrogen at carbon 10, double bond isomerization, and formation of a new carbon-to-oxygen bond. In the case of 15(S)-HPETE, two 8,15- and an erythro-14,15-dihydroxy acid (8,15- and 14,15-DiHETEs), which result from incorporation of molecular oxygen into each hydroxyl group, are coproducts in the formation of 14,15-LTA4. These facts prompted us to test the hypothesis that the biosynthesis of 14,15-LTA4 and of 8,15- and 14,15-DiHETEs from 15(S)-HPETE occurs by a mechanism similar to that observed in lipoxygenase reactions. Based on the results presented here, we conclude that the biosynthesis of 14,15-LTA4 and of 8,15- and 14,15-DiHETEs from 15(S)-HPETE occurs via a common intermediate and that, moreover, the formation of these metabolites from 15(S)-HPETE is catalyzed by an enzyme with many mechanistic features in common with the 12-lipoxygenase.

Nuclear beta decay induced by intense electromagnetic fields: Basic theory

A basic formalism is developed for the theory of the effect on nuclear beta decay of an intense, plane-wave electromagnetic field. Interactions of the field with both the nuclear particles and the decay electron are included. The formalism is developed from first principles, including a derivation of transition probabilities between explicitly time-dependent asymptotic states. Interaction of the field with the nucleus is analyzed in terms of separation of the nucleus into an inert core and a fragment. The field interacts with the fragment, consisting of the nucleons which are candidates for beta decay, plus any other nucleons angular-momentum coupled to them in initial or final states. A separation of variables in the dynamical equations for the nucleus into center-of-mass and relative coordinates for the core and fragment shows direct charge coupling even for a fragment consisting entirely of neutrons. The transition formalism involves specific intense-field wave functions both for the nucleus and for the beta particle. Complete results are presented for total transition probability per unit time for intense-field-coupled nuclear beta decay. A much simplified formalism is given for the special case of very high field intensity at very low frequency. The results then bear a formal resemblance to ordinary beta decay theory, but they contain specific field effects in the beta particle spectral function, and in the nuclear interaction matrix elements. This is the first of a series of papers on this subject.RADIOACTIVITY Intense-field-induced $\ensuremath{\beta}$ decay. $\ensuremath{\beta}$ decay forbiddenness removal.

Positivity improving operators and hypercontractivity

Here (1.1) is the famous Nelson hypercontractivity inequality [14], which has proved to be extremely useful in Euclidean quantum field theory (see e.g. [16]). Like (1.1) the estimate (1.2) follows very easily from the It6 calculus of Brownian motion [3]. Here, in order to make the paper self-contained and to introduce the reader to some general principles of interest, we submit a new proof of (1.2) by mimicing a standard proof of (1.1). We should like to add that (1.2) has at least a formal resemblance to the familiar correlation inequalities from statistical mechanics (see e.g. [11, 12, 16]). Using (1.1) and (1.2) it is simple to obtain similar estimates for the biquantization of a linear contraction on Hilbert space (Sect. 4). Now suppose A is a self-adjoint operator on L 2 of a probability space and set A(A)=maxspec(A)-sup(spec(A)\{maxspec(A)}), where spec(A) denotes the spectrum of A. Below we will state conditions that guarantee that the gap A (A) is proper. In fact, a simplified version of our main result (Theorem 5.3) gives a positive numerical lower bound of A (A) if (i) A is positivity preserving, (ii) sup { IlZf I1~; [I f [12 = 1 } = K 2, and (iii) inf{ [IZfllp/~v_~; I l f l l , = 1, f>0} = k > 0 some 0 < p < 1. Here (i)-(iii) imply that A has a unique ground state. It shall be empha-

Evaluation of the optimal path in ATDHF theory

The formal resemblance between the adiabatic time-dependent Hartree-Fock (ATDHF) theory of Villars and of Baranger and Vénéroni (BV) has been demonstrated. While the BV approach mixes the zeroth- and second-order quantities. Villars neglects the second-order equation and suggests a self-consistent method of solving the zeroth- and first-order equations. It is shown here that in order to obtain the time evolution of the TDHF solution one has to include the second-order equation along with zeroth- and first-order equations. It is then shown by an analytic method that the consistent solutions of the three equations follow the bottom of the valley of the collective potential.

A variational formulation of multiple scattering in muffin-tin alloys

The authors develop a method for the band calculation of muffin-tin alloys which is as simple as the Korringa-Kohn-Rostoker (KKR) method for pure crystals. They begin by postulating Bloch-like basis functions, minimise the energy and arrive at a secular matrix with a formal resemblance to the secular matrix of the average t-matrix approximation (ATA) method. The density of energy states is derived from an argument based on the number of orthogonal basis functions. Using a similar argument, they derive an expression for the energy variance of the Bloch-like states. The advantage of the method is its extreme simplicity: an alloy calculation actually becomes as simple as a band structure calculation for a pure crystal. The method is also extended to situations in which it is feasible to increase the precision of the calculation by working with unit cells with more than one atomic site. Finally, the method is applied to a unidimensional alloy and compared favourably to a CPA and to a Monte Carlo calculation.

General aspects of stochastic quantum field theory for extended particles

Theories of free fields describing spin zero and1/2 extended particles are derived within the stochastic quantum field theory (SQFT) framework. Covariant SQFT analogs of free Schwinger functions and Feynman propagators are obtained, and explicit expressions for charge and four-momentum operators are derived which exhibit a remarkable formal resemblance to their local counterparts. It is shown that the essential results of the LSZ formalism for interacting fields also have their counterpart in SQFT, and that the same holds true of Wightman's reconstruction theorem. Fields on quantum space-time do not obey the local (anti)-commutativity postulate, but we argue that due to the uncertainty principle this postulate cannot be operationally justified as an expression of microcausality despite the customary identification of the two notions. An operationally consistent microcausality condition is proposed instead.

Singular potentials and the divergence problem in quantum field theory

The classification of quantum field theories in superrenormalizable, renormalizable and nonrenormalizable theories corresponds in potential theory to a classification of potentials according to their singular behaviour at the origin. For potentials which are equally or more singular than the «kinetic repulsion» arising from quantum motion, the wave functions obey boundary conditions at the origin different from those of the free solutions. A perturbative approach, therefore, in general, fails which is formally reflected in the occurrence of divergences similar to those in the field-theoretical case. The present investigation seems to indicate that this formal resemblance actually arises from a common origin. On the basis of this apparent analogy, the knowledge of the exact solutions in potential theory suggests possible nonperturbative methods which may avoid the divergences in renormalizable field theories.

A string model of mesons

A string-type meson model with two massive quarks is presented. It is solved exactly by means of almost periodic functions in 3 + 1 space-time dimensions. The solutions, Poincaré generators, and Hamiltonian bear formal resemblance to the corresponding free string quantities. The leading (rising) Regge trajectory is linear but has negative intercept. The degeneracy of the spectrum is greatly reduced and the breaking of reparametization invariance by the non-zero quark masses requires an asymptotic application of the gauge conditions of Virasoro in order that the physical subspace of the usual Nambu string be obtained in the massless limit. Modifications necessary to construct more realistic models and their extensions to baryons are indicated.

Variational approach to quark confinement in field theory

We explore the use of the variational principle in a relativistic field theory of quarks coupled linearly to real scalar gluons. Renormalization is discussed, in principle and in practice. In the actual calculation the theory is cut off at a large but fixed momentum $\ensuremath{\Lambda}$, and variations are performed before taking the limit $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$. Trial wave functions are such that quarks find themselves in a central scalar square-well potential. The outside mass ${M}_{0}$ the inside mass ${M}_{1}$, and the range ${r}_{0}$ are variational parameters. By construction the wave functions are eigenstates of total momentum and angular momentum, and form a complete set. In the limit of infinite renormalized gluon mass the entire calculation can be done analytically, with the following results. There is a choice of model constants such that ${M}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ in the renormalized limit. Futhermore, the model constants can be so chosen that the calculation reduces to one that bears formal resemblance to calculations in a classical field theory. We examine in greater detail this "semiclassical" limit, and, in particular, investigate two consistent possibilities that are similar respectively to the MIT bag model and the SLAC model. In either case the model still contains two free renormalized constants. Depending on their values there may or may not be a vacuum well (i.e., ${M}_{1}\ensuremath{\ne}{M}_{0}$ in the lowest state). Illustrations of physical applications are given in the MIT case. Hadronic structure and nucleon deep-inelastic structure functions are calculated, with results similar to those of the MIT bag model. In particular, the structure functions exhibit scaling.

The waveguide mode theory of propagation of ELF electromagnetic waves over the spherical surface of the Earth

The theoretical formulation of the propagation of ELF radio waves, which can be used for the study of Schumann resonances, is developed without making use of the Debye-Watson approximation for the Hankel functions. The modal equations thus obtained are compared with those for a plane wave in a planar waveguide to show that there is a formal resemblance between the two but that the planar approximation does not hold in a strict physical sense. The thin shell approximation leads to the same formulation as the planar approximation if we assume that v( v + 1) = ( k 0 aS) 2.

Pulse-induced critical scattering (PICS) from polymer solutions

Abstract