x-ray diffraction peak profile analysis was used to identify changes in the lattice distortions during isothermal aging of fe-10ni-7mn (wt. %) maraging steel. integral peak breadths were analyzed using classical williamson-hall equation taking the elastic anisotropy into account. it was found that substantial lattice distortions rise during precipitation hardening which depend strongly on the s...

we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

  Nonlinear Dust lattice modes are studied in a hexagonal two-dimensional dusty plasma lattice, in presence of charge gradient of dust particles. In this lattice, such gradients affect nonlinear behavior of dust lattice waves. The amplitude modulation of off-plane transverse dust lattice wave packets is investigated considering the anisotropy of interactions, caused by the height-dependent char...

A well-known result of universal algebra states: every algebraic lattice is isomorphic to the congruence lattice of an algebra. It is natural to ask whether every finite lattice occurs as the congruence lattice of a finite algebra. This fundamental question, asked over 45 years ago, is among the most elusive problems of universal algebra. Call a finite lattice L “representable” if it is the con...

We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL2(F41)⊗ S̃3 ⊂ GL80(Z) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ-series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite...

Subgroups of the symmetric group Sn act on powers of chains C n by permuting coordinates, and induce automorphisms of the ordered sets C. The quotients defined are candidates for symmetric chain decompositions. We establish this for some families of groups in order to enlarge the collection of subgroups G of the symmetric group Sn for which the quotient Bn/G obtained from the G-orbits on the Bo...

We show that the number of rational points a subgroup inside toric variety over finite field defined by homogeneous lattice ideal can be computed via Smith normal form matrix whose columns constitute basis lattice. This generalizes and yields concise geometric proof same fact proven purely algebraically Lopez Villarreal for case projective space standard dimension one. also prove Nullstellensat...