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In this paper, firstly, the concept of a new type of derivations on FI-algebras is introduced. The existence of it is verified by an example and a program. Then, the concepts of different kinds of derivations on FI-algebras are given. The properties of derivations on FI-algebras and the relationship between derivations and ideal are investigated. The equivalent conditions of identity derivation and the equivalent conditions of isotone derivation are proved. Finally, the concept of \(a-\)principal derivations on DFI-algebras is given. The existence of \(a-\)principal derivations is verified by an example and a program.

Intuitionistic Fuzzy Implication plays an important role in Intuitionistic Fuzzy reasoning and decision making. In this paper I extend Lukasiewicz’s type implication operator (⇒LK) to Intuitionistic Fuzzy Matrix(IFM). Boundary conditions, isotone and antitone of implication operator are verified. The relation between Lukasiewicz’s type conjunction (⊙), disjunction (⊕) and implication operator (⇒LK) are constructed. Finally we conclude the algebraic structure (𝔍Fmn, ≤, ∨, ∧, ⊕, ⇒LK, U, O) satisfy all the properties of a residuated lattice except the converse part of adjoint pair on IFMs.

We provide an approach to one-sided (crisp-fuzzy) concept lattices based on isotone Galois connections. Isotone Galois connections and concept lattices provide an alternative to the classical, antitone Galois connections based concept lattices, which are fundamental structures in formal concept analysis of object-attribute models with many-valued attributes. Our approach is suitable for analysis of data tables with different structures for truth values of particular attributes. A possible applications of this approach for approximation of object subsets is also presented.

Let X be a partially ordered finite set with a partial order $<

In the paper the concept of covering (regularity) for set-valued mappings in partially ordered spaces is introduced. The coincidence points problem for set-valued mappings in partially ordered spaces is considered. Sufficient conditions for the existence of coincidence points of isotone and orderly covering set-valued mappings are obtained. It is shown that the known theorems on coincidence points of covering and Lipschitz mappings in metric spaces can be deduced from the obtained results.

The aim of this paper is to introduce the notion of ageneralized derivations of BCH-algebras and some related proper-ties are investigated. 1. IntroductionIn 1966, Imai and Iseki introduced two classes of abstract algebras,BCK-algebra and BCI-algebras [6]. It is known that the class of BCI-algebras is a generalization of the class of BCK-algebras In 1983, Hu andLi [3] introduced the notion of a BCH-algebra, which is a generalizationof the notions of BCK-algebras and BCI-algebras. They have studied afew properties of these algebras. In this paper, we introduce the notion ofgeneralized derivations of BCH-algebras and investigate some propertiesof generalized derivations in a BCH-algebra. Moreover, we introducethe notions of xed set and kernel set of generalized derivations in aBCH-algebra and obtained some interesting properties in medial BCH-algebras. Also, we discuss the relations between ideals in a medial BCH-algebras.2. PreliminaryBy a BCH-algebra, we mean an algebra (X;;0) with a single binaryoperation \" that satis es the following identities for any x;y;z2X:(BCH1) xx= 0

In this paper we obtain sufficient conditions for the existence of fixed point of T-isotone mappings and coincidence point of G-isotone mappings in partially ordered metric spaces.

In this paper, we introduce the notion of multiderivations on lattices and their fixed sets. By using the superjoinitivity and supermeetability properties of the multifunctions, we give some new results on properties of isotone and joinitive multiderivations on lattices. In this way, we show that under some conditions the fixed set of a multiderivation is an ideal.

Using the well-known equivalence between meet-completions of posets and standard closure operators we show a general method for constructing meet-completions for isotone poset expansions. With this method we find a meet-completion for ordered domain algebras which simultaneously serves as the base of a representation for such algebras, thereby proving that ordered domain algebras have the finite representation property. We show that many of the equations defining ordered domain algebras are preserved in this completion but associativity, (D2) and (D6) can fail.

The level structures of the very neutron-rich nuclei 128Pd82 and 126Pd80 have been investigated for the first time. A new isomer with a half-life of 5.8(8) μs in 128Pd is proposed to have a spin and parity of 8+ and is associated with a maximally aligned configuration arising from the g9/2Pd proton subshell with seniority υ = 2. The level sequence below the 8+ isomer is similar to that in the N = 82 isotone 130Cd, but the electric quadrupole transition that depopulates the 8+ isomer is more hindered in 128Pd than in 130Cd, as expected in the seniority scheme for a semi-magic, spherical nucleus. For 126Pd, three new isomers with Jπ = (5-), (7-), and (10+) have been identified with half-lives of 0.33(4) μs, 0.44(3) μs, and 23.0(8) ms, respectively. The smaller energy difference between the 10+ and 7- isomers in 126Pd than in the heavier N = 80 isotones can be interpreted as being ascribed to the monopole shift of the h11/2 neutron orbit. The nature of the N = 82 shell closure scrutinized with these characteristic isomers is discussed.

The high-K isomeric states in light superheavy nuclei around A = 250 mass region are investigated by the Cranked Shell Model (CSM) with pairing treated by a Particle-Number Conserving (PNC) method. With including the higher-order deformation ε6, both of the high–K multi-particle state energies and the rotational bands in 254No and N = 150 isotone are reproduced well. The isomeric state energies and the microscopic mechanism of kinematic moment of inertia variations versus rotational frequency are discussed. The irregularity of the two-neutron Kπ = 8- state band at ħω ≈ 0:17 in 252No is caused by the configuration mixing with the two-proton Kπ = 8- band. .

In this paper, we introduce the notion of derivations for a trellis and investigate some related properties of this subject. We give some equivalent conditions under which a derivation is isotone for trellises. Also, we study fixed points and define f-derivation on T and Cartesian derivation on T1 × T2.

WOS: 000454271700012, In this paper, we introduced the notion of multiplier of a hyper BCC-algebra, and investigated some properties of hyper BCC- algebras. And then we introduced notion of kernels and notion of hyper normal ideal of multipliers on hyper BCC-algebras. Also we gave some propositions related with isotone and Fix(d)(H).

In this paper, we introduce the notion of f-derivation in a BE- algebra, and consider the properties of f-derivations. Also, we characterize the flxed set Fixd(X) and Kerd by f-derivations. Moreover, we prove that if d is a f-derivation of a BE-algebra, every f-fllter F is a a d-invariant.

In the present paper we introduced the notion of (θ ,φ)-derivations of a BCI-algebra X . Some interesting results on inside (or outside) (θ ,φ)-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X , every inside (θ ,φ)derivation of X is isotone. Furthermore it is also proved that for any outside (θ ,φ)-derivation d(θ ,φ) of a BCI-algebra X , d(θ ,φ)(x) = θ (x)∧d(θ ,φ)(x) if and only if d(θ ,φ)(0) = 0 for all x ∈ X .

The concept of covering (regularity) for mappings in partially ordered spaces is introduced. Sufficient conditions for the existence of coincidence points and minimal coincidence points of isotone and orderly covering mappings are obtained. These results generalize classical fixed point theorems for isotone mappings. Moreover, the known theorems on coincidence points of covering and Lipschitz mappings in metric spaces are deduced from the obtained results.

For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-partitions. To any poset ideal ${\mathcal J}$ in $\text{Hom}(P,\mathbb{N})$, finite or infinite, we associate monomial ideals: the letterplace ideal $L({\mathcal J},P)$ and the Alexander dual co-letterplace ideal $L(P,{\mathcal J})$, and study them. We derive a class of monomial ideals in $k[x_p, p \in P]$ called $P$-stable. When $P$ is a chain we establish a duality on strongly stable ideals. We study the case when ${\mathcal J}$ is a principal poset ideal. When $P$ is a chain we construct a new class of determinantal ideals which generalizes ideals of {\it maximal} minors and whose initial ideals are letterplace ideals of prinicpal poset ideals., 29 pages

In this paper, we introduce the concept of isotone cones in Banach spaces. Then we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity conditions in partially ordered Banach spaces., 23 pages

New excited states in $^{142}$Ba and $^{144}$Ce are investigated by means of prompt $\gamma$-ray spectroscopy of the radiation following spontaneous fission of $^{252}$Cf. Measurements of angular correlations and the observed branchings allowed the assignment of spins and parities with confidence. The new measurements are reinforced by shell-model calculations where energy levels, electric transitions, and magnetic moments are consistent with experimental data. The presence of collectivity in the N=86 isotones is confirmed by clear signatures of soft triaxial γ bands in both nuclei.

Spin-orbit splitting is an essential ingredient for our understanding of the shell structure in nuclei. One of the most important advantages of relativistic mean-field (RMF) models in nuclear physics is the fact that the large spin-orbit (SO) potential emerges automatically from the inclusion of Lorentz-scalar and -vector potentials in the Dirac equation. It is therefore of great importance to compare the results of such models with experimental data. We investigate the size of $2p$ and $1f$ splittings for the isotone chain $^{40}$Ca, $^{38}$Ar, $^{36}$S, and $^{34}$Si in the framework of various relativistic and nonrelativistic density functionals. They are compared with the results of nonrelativistic models and with recent experimental data., 19 pages, 10 figures

The $\ensuremath{\beta}$-decay properties of the very neutron-rich nucleus $^{85}\mathrm{Ge}$, produced in the proton-induced fission of $^{238}\mathrm{U}$, were studied at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. The level scheme of $\phantom{\rule{0.16em}{0ex}}_{33}^{85}\mathrm{As}_{52}$ populated in $^{85}\mathrm{Ge}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}\ensuremath{\gamma}$ decay was reconstructed and compared to shell-model calculations. The investigation of the systematics of low-energy levels in $N=52$ isotones together with shell-model analysis allowed us to provide an estimate of the low-energy structure of the more exotic $N=52$ isotone $^{81}\mathrm{Cu}$.

In this paper, we introduce the concept of a rightderivation in incline algebras and give some properties of inclinealgebras. Also, the concept of d-ideal is introduced in an inclinealgebra with respect to right derivation. 1. IntroductionZ. Q. Cao, K. H. Kim and F. W. Roush [4] introduced the notionof incline algebras in their book and later it was developed by someauthors [1, 2, 3, 5]. Ahn et al [1] introduced the notion of quotientincline and obtained the structure of incline algebras. N. O. Alshehri [3]introduced the notion of derivation in incline algebra. Incline algebra is ageneralization of both Boolean and fuzzy algebra and it is a special typeof semiring. It has both a semiring structure and a poset structure. Itcan also be used to represent automata and other mathematical systems,to study inequalities for non-negative matrices of polynomials. In thispaper, we introduce the concept of a right derivation in incline algebrasand give some properties of incline algebras. Also, the concept of d-idealis introduced in an incline algebra with respect to right derivation.2. PreliminariesAn incline algebra is a set K with two binary operations denoted by\ + " and \ " satisfying the following axioms:(K1) x+ y = y + x;(K2) x+ (y + z) = (x+ y) + z

Fast-rotating N = 151 isotones 245 Pu, 247 Cm and 249 Cf have been studied through inelastic excitation and transfer reactions with radioactive targets. While all have a ground-state band built on a ν j 15 / 2 [ 734 ] 9 / 2 − Nilsson configuration, new excited bands have also been observed in each isotone. These odd- N excited bands allow a comparison of the alignment behavior for two different configurations, where the ν j 15 / 2 alignment is either blocked or allowed. The effect of higher order deformations is explored through cranking calculations, which help clarify the elusive nature of ν j 15 / 2 alignments.

Triadic concept analysis is a method of analysis of three-way tabular data describing objects by binary attributes they have under various conditions. It aims to extract a set of three-dimensional clusters, so-called triadic concepts, from the data. While the method was recently extended to handle the case of graded data, this extension is only one of a variety of possible generalizations, namely the one where the so-called antitone concept-forming operators are considered. The generalizations not covered by the mentioned approach include isotone concept-forming operators, one sided concepts, the use of truth stressing hedges and many others. Since all of the generalizations have their applications, for example in factor analysis of relational data, it is desirable to have a uniform mathematical foundations covering all of the cases. In this paper we provide such foundations. By using triadic aggregation structures as a scale of truth degrees we develop triadic concept analysis in a very general setting that covers a wide variety of its possible extensions in a uniform way.

This note gives a complete characterization of when the ordinal sum of two lattices (the lattice obtained by placing the second lattice on top of the first) is projective. This characterization applies not only to the class of all lattices, but to any variety of lattices, and in particular, to the class of distributive lattices. Lattices L with the property that every epimorphism onto L has an isotone section are also characterized.

Previous work gives algebras for uniformly describing correctness statements and calculi in various relational and matrix-based computation models. These models support a single kind of non-determinism, which is either angelic, demonic or erratic with respect to the infinite executions of a computation. Other models, notably isotone predicate transformers or up-closed multirelations, offer both angelic and demonic choice with respect to finite executions. We propose algebras for a theory of correctness which covers these multirelational models in addition to relational and matrix-based models. Existing algebraic descriptions, in particular general refinement algebras and monotonic Boolean transformers, are instances of our theory. Our new description includes a precondition operation that instantiates to both modal diamond and modal box operators. We verify all results in Isabelle, heavily using its automated theorem provers. We integrate our theories with the Isabelle theory of monotonic Boolean transformers making our results applicable to that setting.

The present paper gives the notion of a derivation on a CI-algebra X and investigates related properties. We deflne a set Fixd(X) by Fixd(X) = fx 2 X j d(x) = xg, where d is a derivation on a CI-algebra X. We show that Fixd(X) is a subalgebra of X. Also, we prove some one-to-one and onto derivation theorems. Moreover, we study a regular derivation on a CI-algebra and an isotone derivation on a transitive CI-algebra.

In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of gen- eralized derivations. Also, we characterize the flxed set Fixd(X) and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every fllter F is a d-invariant.

In this paper, we introduce the notion of derivationin a BE-algebra, and consider the properties of derivations. Also,we characterize the xed set Fix d (X) and Kerd by derivations.Moreover, we prove that if d is a derivation of BE-algebra, every lter F is a d-invariant. 1. IntroductionY. Imai and K. Is eki introduced two classes of abstract algebras:BCK-algebras and BCI-algebras([3, 4]). It is known that the class ofBCK-algebras is a proper subclass of the class of BCI-algebras. In [1,2], Q. P. Hu and X. Li introduced a wide class of abstracts: BCH-algebras. They have shown that the class of BCI-algebras is a propersubclass of the class of BCH-algebras. In [5], H. S. Kim and Y. H. Kimintroduced the notion of a BE-algebra as a dualization of a generation ofa BCK-algebras. In this paper, we introduced the notion of derivationin a BE- algebra, and considered the properties of derivations. Also, wecharacterized the xed set Fix d (X) and Kerd by derivations. Moreover,we prove that if d is a derivation of BE-algebra, every lter F is a d-invariant.2. PreliminariesIn what follows, let X denote an BE-algebra unless otherwise speci- ed.

Multirelations model computations with both angelic and demonic non-determinism. We extend multirelations to represent finite and infinite computations independently. We derive an approximation order for multirelations assuming only that the endless loop is its least element and that the lattice operations are isotone. We use relations, relation algebra and RelView for representing and calculating with multirelations and for finding the approximation order.

The aim of this present work is to generalize the notion of weakly isotone increasing mappings and prove an α- fixed point theorems for α -weakly isotone increasing self mappings which satisfy some inequality in complete metric spaces endow with partially ordering.

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility, and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.

New level schemes of 112,114,115,116,117,118Pd are established by means of γ – γ – γ , γ – γ – γ – γ and γ – γ ( θ ) measurements of prompt fission γ rays from 252Cf using the Gammasphere multi-detector array. Spins/parities were assigned to levels based on γ – γ angular correlation measurements, level systematics and decay patterns. In the even-N isotopes 112,114,116Pd, two sets of odd-parity bands were identified and extended with spins measured in each band. The odd-parity bands with large level staggerings were interpreted as disturbed chirality with less pronounced triaxial deformations in the Pd isotopes than observed in the chiral symmetry breaking 110,112Ru with maximum triaxiality. Onset of wobbling motion was identified from the sign of the signature splitting in the γ band of even–even 114Pd, and probably also in 116Pd, as first seen in the N = 68 isotone 112Ru. Maximal triaxiality in Ru and Pd isotopes is found to be reached for N = 68 , 112Ru and 114Pd, 4 neutrons more than predicted in the theoretical calculations. The new data and TRS calculations allowed a systematic study of the band crossings in the even-N 112,114,116Pd and odd-N 115,117Pd isotopes. Now we find a new overall, more complex shape evolution than previously proposed from triaxial prolate in 110Pd via triaxial oblate in 112Pd to nearly oblate in 114,116Pd with a large change of the triaxial deformation parameter γ toward nearly oblate in the ( π g 9 / 2 ) 2 alignment in 114,115,116,117,118Pd, and triaxial-prolate–triaxial-oblate shape coexisting bands in 115Pd.

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

In this paper, we introduce the new notion which is more general than the previous works on the weakly isotone mappings in the case of single valued mappings and multivalued mappings in an ordered Banach space. We also extend some common fixed point theorems of Dhage et al. [4] and give some applications of the main results. Furthermore, at the end of this paper, we give an open problem for further investigation.

By using some lattice-like operations which constitute extensions of ones introduced by M.S. Gowda, R. Sznajder and J. Tao for self-dual cones, a new perspective is gained on the subject of isotonicity of the metric projection onto the closed convex sets. The results of this paper are wide range generalizations of some results of the authors obtained for self-dual cones. The aim of the subsequent investigations is to put into evidence some closed convex sets for which the metric projection is isotonic with respect to the order relation which give rise to the above mentioned lattice-like operations. The topic is related to variational inequalities where the isotonicity of the metric projection is an important technical tool. For Euclidean sublattices this approach was considered by G. Isac and respectively by H. Nishimura and E.A. Ok.

A realistic density-dependent nucleon–nucleon (NN) interaction with finite-range exchange part which produces the nuclear matter saturation curve and the energy dependence of the nucleon–nucleus optical model potential is used to calculate the preformation probability, S α , of α-decay from different isotones with neutron numbers N = 124 , 126 , 128 , 130 and 132 . We studied the variation of S α with the proton number, Z, for each isotone and found the effect of neutron and proton energy levels of parent nuclei on the behavior of the α-particle preformation probability. We found that S α increases regularly with the proton number when the proton pair in α-particle is emitted from the same level and the neutron level sequence is not changed during the Z-variation. In this case the neutron–proton (n–p) interaction of the two levels, contributing to emission process, is too small. On the contrary, if the proton or neutron level sequence is changed during the emission process, S α behaves irregularly, the irregular behavior increases if both proton and neutron levels are changed. This behavior is accompanied by change or rapid increase in the strength of n–p interaction.

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.

In this paper, we introduced the notion of multiplier of a BCC-algebra, and gave some properties of BCC-algebras. Also, we characterized kernels and normal ideals of multipliers on BCC-algebras.

Let X be a partially ordered set and O(X) be the semigroup of all mappings X → X that preserve the order, i.e., x ≤ y ⟹ xα ≤ yα for all x, y ∈ X. It is proved that the semigroup O(X) is weakly regular in the wide sense if and only if at least one of the following conditions holds: (1) X is a quasi-complete chain; (2) the elements of X are not comparable pairwise; (3) X = Y ∪ Z, where y < z for y ∈ Y, z ∈ Z; (4) X = Y ∪ Z, where y0 ∈ Y, z0 ∈ Z, and y0< z for z ∈ Z, y < z0 for y ∈ Y; (5) X = {a, c} ∪ B, where a < b < c for b ∈ B; (6) X = {1, 2, 3, 4, 5, 6}, where 1 < 4, 1 < 5, 2 < 5, 2 < 6, 3 < 4, 3 < 6. Moreover, if X is a quasi-ordered set but not partially ordered, then the semigroup O(X) is weakly regular in the wide sense if and only if x ≤ y for all x, y ∈ X.

Common fixed point theorems for T -weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function φ : [ 0 , + ∞ ) → [ 0 , + ∞ ) with φ ( t ) t for each t > 0 and φ ( 0 ) = 0 in complete ordered partial metric spaces are proved. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples.

For the case of classical Tarski’s theorem on fixed points of isotone maps we show that embedding of this statement into fuzzy logical environment leads to surprising results, which cannot be easily seen and awaited in classical logical environment.