Nuclear Liquid Drop Model with the Surface-Curvature Terms: New Perspectives for the Hyperdeformation Studies

Nuclear liquid drop model is revisited and an explicit introduction of the surface-curvature terms is presented. The corresponding parameters of the extended classical energy formula are adjusted to the contemporarily known nuclear binding energies and fission barrier heights. Using 2766 binding energies of nuclei with $Z\geq 8$ and $N\geq 8$ it is shown that the performance of the new approach is improved by a factor of about 6, compared to the previously published liquid drop model results, in terms of both the masses (new r.m.s. deviation $= 0.698$ MeV) and the fission barriers (new r.m.s. deviation of the fission barriers of isotopes with $Z> 70$ is $<\delta V_B> = 0.88$ MeV). The role of the curvature terms and their effects on the description of the experimental quantities are discussed in detail; for comparison the parameters of the more 'traditional' approaches are re-fitted taking into account the nuclear masses known today and the performances of several variants of the model are compared. The isospin dependence in the new description of the barriers is in a good agreement with the extended Thomas-Fermi approach; it also demonstrates a good qualitative agreement with the fission life-time systematics tested on the long chain of Fermium isotopes known experimentally. The new approach offers also a very high stability in terms of the extrapolation from the narrower range of nuclides to a more extended one - a property of particular interest for the contemporary exotic beam projects: the corresponding properties are illustrated and discussed.Comment: 25 pages in LaTeX and 20 figures in eps forma

Expectation Formation and Endogenous Fluctuations in Aggregate Demand

The paper recognizes that expectations and the process of their formation are subject to standard decision making and are determined as a part of equilibrium. Accordingly, the paper presents a basic framework in which the form of expectation formation is a choice variable. At any point in time rational economic agents decide on the basis of the level of utility what expectation formation technology to use and as a consequence what expectations to hold. As economic decisions are conditioned on expectations holding proper or rational expectations eliminates the possibility of ex ante inefficiencies. The choice of expectation formation technology is not trivial as the paper assumes that information gathering and processing are costly. Consequently, economic agents must make informed decisions with the regard to the quality of expectation formation technologies they wish to use. The paper shows that agents' optimization over expectations not only adds on to realism, but also can carry non trivial implications for the behavior of macroeconomic variables. Specifically, the paper illustrates that endogenous expectation revisions can be a source of permanent oscillations in aggregate demand and can prevent an economy from settling into a steady state. In addition, the paper quantifies intangible notions such as overheating, overborrowing, and output gap. Finally, the paper shows that active policy measures can limit inefficiencies resulting from output fluctuationsBusiness Cycles, Expectation Formation, Costly Information Acquisition.

A description of n-ary semigroups polynomial-derived from integral domains

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the corresponding ternary semigroups

Interaction Strengths for the Fock-Space Formulation of the Nuclear Pairing Problem

A realistic nuclear mean-field hamiltonian with pairing has been diagonalized using Fock space representation that allows for nearly exact treatment of the problem. Calculations were performed for all the even-even nuclei with Z in (20, 100), whose pairing gaps were possible to extract out of the experimental masses. The optimal values of the pairing strength constants for the protons and neutrons have been found.Comment: Seminar given at XXXVII School of Physics in Zakopane, Poland. Paper in LaTeX, 4 pages including one figure, submitted to Acta Physica Polonica

Subtraction Menger algebras

Abstract characterizations of Menger algebras of partial $n$-place functions defined on a set $A$ and closed under the set-theoretic difference functions treatment as subsets of the Cartesian product $A^{n+1}$ are given

On Artificial Structural Unemployment

Above market clearing wages are shown to prevail as an outcome of a game in which employers possess and employees lack the ability to coordinate. It is established in a monopolistically competitive framework that it may be optimal for individual firms to coordinate and restrict entry of indirect competitors and thus increase profits by paying above market clearing wages as the higher wage bill need not outweigh the increase in profits due to entry restriction. Resulting unemployment is shown to be socially costly. The paper notes that a tax on revenue of the incumbent firms can be welfare improvingUnemployment, Coordination

Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page