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In this work, we present the notion of a multiplier on AT-algebra and investigate several properties. Also, some theorems and examples are discussed. The notions of the kernel and the image of multipliers are defined. After that, some propositions related to isotone and regular multipliers are proved. Finally, the Left and the Right derivations of the multiplier are obtained

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dua...

In this paper, state operators on hyper BE-algebras (correspondingly, state hyper BE-algebras) are introduced and studied. State hyper filters are introduced and generated state hyper filters are represented in state hyper BE-algebras. Also, maximal (prime) state hyper filters are characterised and the relations between state maximal hyper filters and state prime hyper filters are discussed. Moreover, some related results of state (compatible) hyper congruence are obtained. Especially, it follows that there is an isotone bijection between all state strong regular $circ$-reflexive hyper filter $mathcal{F}_s(H,xi)$ and all state compatible hyper congruence $mathcal{C}_s(H,xi)$ on state commutative transitive RD-hyper BE-algebra $(H,xi)$.

In this paper we define two types of implicative derivations on pseudo-BCK algebras, we investigate their properties and we give a characterization of isotone implicative derivations. The multiplicative derivations on BCK-algebras with product are introduced and investigated as well. At the same time, particular cases of multiplicative derivations are defined and their properties are investigated. Moreover, we prove that two good ideal multiplicative derivations coincide if and only if their corresponding sets of fixed points coincide. We also define the translation and scaling derivation operators, we study their properties and we show that these operators form a residuated pair. Finally, we prove that there exists an order preserving bijection between the fixed points sets of the two operators.

The aim of this paper is to define the monadic quantum B-algebras and to investigate their properties. If the monadic operators are isotone, we show that they form a residuated pair. Special properties are studied for the particular case of monadic quantum B-algebras with pseudo-product, and a representation theorem for monadic quantum B-algebras with pseudo-product is proved. The monadic filters of monadic quantum B-algebras are defined, and their properties are studied. We prove that there is an isomorphism between the lattice of all filters of a monadic quantum B-algebra and the lattice of all filters of its subalgebra of fixed elements. Monadic operators on unital quantales are introduced, and the functional monadic quantale is constructed.

Excited-state lifetimes were measured by direct fast-timing methods in three N = 125 isotones — 209Po, 211Rn, and 213Ra — near doubly magic 208Pb. These nuclei have a single neutron hole and successively add pairs of protons relative to 208Pb. The first-excited state to ground-state transition, 5 / 2 1 − → 1 / 2 1 − , has almost identical energy in each isotone and can be associated with the single neutron-hole transition ν f 5 / 2 − 1 → ν p 1 / 2 − 1 . The extent to which the protons act as spectators is assessed based on the measured transition rates, which show a systematic increase along the isotone chain, and by comparisons with large-basis shell-model calculations. The shell model accounts for some of the increased transition strength but consistently underestimates the experimental values. It also fails to explain the near-constant transition energies. These results suggest emerging collectivity beyond the shell-model valence space and show that the near-constant transition energies are not a consequence of a pure neutron-hole transition, but rather the outcome of complex nucleon-nucleon correlations that increase quadrupole collectivity.

The paper deals mainly with a fuzzification of the classical Tarski's theorem for commutative sets of isotone maps (the so-called generalized theorem) in a sufficiently rich fuzzy setting on general structures called L-complete propelattices. Our concept enables a consistent analysis of the validity of single statements of the generalized Tarski's theorem in dependence on assumptions of relevant versions of transitivity (weak or strong). The notion of the L-complete propelattice was introduced in connection with the fuzzified more famous variant of Tarski's theorem for a single L-fuzzy isotone map, whose main part holds even without the assumption of any version of transitivity. These results are here extended also to the concept of the so-called L-fuzzy relatively isotone maps and then additionally compared to the results, which are achieved for the generalized theorem and which always need a relevant version of transitivity. Wherever it is possible, facts and differences between both the theorems are demonstrated by appropriate examples or counterexamples.

The set of necessary and sufficient conditions under which an isotone mapping from a subset of a poset X to a poset Y has an isotone extension to an isotone mapping from X to Y is found.

As is known, the Hardy–Littlewood–Polya submajorization preorder among integrable real-valued functions separates into the concatenation of pointwise inequality and majorization, in this order, i.e., if $$ x\prec \prec y$$ , then there is a z with $$x\le z\prec y$$ . Submajorization also separates, in the other order, into majorization and inequality, i.e., if $$x\prec \prec y$$ , then there is a w with $$x\prec w\le y$$ and, as is shown here, such a w can be chosen to be nonnegative if both x and y are. It is also shown that the former separation result (existence of z) can be deduced from the latter one (existence of w) by using a doubly stochastic operator on the Banach space $$L^{\varrho }\left( T\right) $$ , where T is a finite measure space and $$\varrho \in \left[ 1,+\infty \right] $$ . The results are applied to a $$\prec \prec $$ -isotone real-valued function C on the nonnegative cone $$ L_{+}^{\varrho }\left( T\right) $$ and to its positive-part extension to all of $$L^{\varrho }\left( T\right) $$ , defined by $$C^{\dagger }\left( y\right) =C\left( y^{+}\right) $$ , whose economic interpretation, when $$ C\left( y\right) $$ is the joint cost of producing quantities $$\left( y\left( t\right) \right) _{t\in T}$$ of a spectrum of commodities, is that of adding free disposal to the technology.

We have carried out a systematic study of F-spin multiplets having similar product of their valence nucleons (i.e., N p N n -values) to extract the prominent features which are responsible in generating the identical rotational bands among them. It has been established by us from the experimental data of rare-earth region that a subsequent addition of proton pair in an isotonic set of nuclei increases their (i.e., isotones) pairing contribution whereas a reversing trend has been seen while adding a neutron pair in an isotopic set. Similar type of opposite trends have also been observed in their quadrupole deformations while adding a pair of proton and neutron, respectively, in an isotone and isotope. Thus, a simultaneous addition of both proton and a neutron pair in any one of the F-spin multiplet does not alter the pairing contribution as well as deformation structure of a newly emerging F-spin multiplet provided these multiplets belong to generalized mirror pair having same N p N n products and hence the identicity prevails between their rotational spectra. These experimentally observed opposing trends of pairing correlations and deformation parameters with the addition of a particular nucleon pair in an isotone and isotope, respectively, are also supported by our cranking model calculations. These systematic studies together with the cranking model calculations have further been extended to explore the possibilities of obtaining the identical band structures between odd-A and neighboring even-even nuclei.

In a recent paper, Çeven and Öztürk have generalized the notion of derivation on a lattice to f-derivation, where f is a given function of that lattice into itself. Under some conditions, they have characterized the distributive and modular lattices in terms of their isotone f-derivations. In this paper, we investigate the most important properties of isotone f-derivations on a lattice, paying particular attention to the lattice (resp. ideal) structures of isotone f-derivations and the sets of their f-fixed points. As applications, we provide characterizations of distributive lattices and principal ideals of a lattice in terms of principal f-derivations.

We report high-precision mass measurements of $^{50--55}\mathrm{Sc}$ isotopes performed at the LEBIT facility at NSCL and at the TITAN facility at TRIUMF. Our results provide a substantial reduction of their uncertainties and indicate significant deviations, up to 0.7 MeV, from the previously recommended mass values for $^{53--55}\mathrm{Sc}$. The results of this work provide an important update to the description of emerging closed-shell phenomena at neutron numbers $N=32$ and $N=34$ above proton-magic $Z=20$. In particular, they finally enable a complete and precise characterization of the trends in ground state binding energies along the $N=32$ isotone, confirming that the empirical neutron shell gap energies peak at the doubly magic $^{52}\mathrm{Ca}$. Moreover, our data, combined with other recent measurements, do not support the existence of a closed neutron shell in $^{55}\mathrm{Sc}$ at $N=34$. The results were compared to predictions from both ab initio and phenomenological nuclear theories, which all had success describing $N=32$ neutron shell gap energies but were highly disparate in the description of the $N=34$ isotone.

Albergo thermometers with double isotope, isotone, and isobar yield ratio pairs with one proton and/or neutron difference are investigated. Without any extra sequential decay correction, a real temperature value of $4.9\ifmmode\pm\else\textpm\fi{}0.5$ MeV is deduced from the yields of the experimentally reconstructed primary hot intermediate mass fragments (IMFs) from $^{64}\mathrm{Zn}+^{112}\mathrm{Sn}$ collisions at 40 MeV/nucleon using the Albergo thermometer for the first time. An experimental sequential decay correction from the apparent temperatures to the real ones for 12 other reaction systems with different neutron-proton ($N/Z$) asymmetries in the same experiment, $^{70}\mathrm{Zn}$, $^{64}\mathrm{Ni}$ on $^{112,124}\mathrm{Sn}$, $^{58,64}\mathrm{Ni}$, $^{197}\mathrm{Au}$, and $^{232}\mathrm{Th}$ at 40 MeV/nucleon, is performed using an empirical correction factor approach of Tsang et al. [Phys. Rev. Lett. 78, 3836 (1997)] with the deduced 4.9-MeV temperature value. The dependence of nuclear temperature on the source $N/Z$ asymmetry is further investigated using these deduced real source temperature values from the present 13 systems. It is found that the deduced real source temperatures at the present source $N/Z$ range show a rather weak dependence on the source $N/Z$ asymmetry. By comparison between our previous results and those from other independent experiments, a consistent description for the $N/Z$ asymmetry dependence of nuclear temperature is addressed.

Author(s): Salathe, M; Crawford, HL; Macchiavelli, AO; Kay, BP; Hoffman, CR; Ayangeakaa, AD; Campbell, CM; Clark, RM; Cromaz, M; Fallon, P; Jones, MD; Kuvin, SA; Sethi, J; Wiedeking, M; Winkelbauer, JR; Wuosmaa, AH | Abstract: The excitation energy of deformed intruder states (specifically the 2p2h bandhead) as a function of proton number Z along N=20 is of interest both in terms of better understanding the evolution of nuclear structure between spherical Ca40 and the Island of Inversion nuclei, and for benchmarking theoretical descriptions in this region. At the center of the N=20 Island of Inversion, the npnh (where n=2,4,6) neutron excitations across a diminished N=20 gap result in deformed and collective ground states, as observed in Mg32. In heavier isotones, npnh excitations do not dominate in the ground states but are present in the relatively low-lying level schemes. With the aim of identifying the expected 2p2h - s1/2+ state in P35, the only N=20 isotone for which the neutron 2p2h excitation bandhead has not yet been identified, the S36(d,He3)P35 reaction has been revisited in inverse kinematics with the HELical Orbit Spectrometer (HELIOS) at the Argonne Tandem Linac Accelerator System (ATLAS). While a candidate state has not been located, an upper limit for the transfer reaction cross section to populate such a configuration within a 2.5 to 3.6 MeV energy range provides a stringent constraint on the wave function compositions in both S36 and P35.

The neutron-rich nuclei in the $N=28$ island of inversion have attracted considerable experimental and theoretical attention, providing great insight into the evolution of shell structure and nuclear shape in exotic nuclei. In this work, for the first time, quadrupole collectivity is assessed simultaneously on top of the $3/{2}^{\ensuremath{-}}$ ground state and the $7/{2}^{\ensuremath{-}}$ shape-coexisting isomer of $^{43}\mathrm{S}$, putting the unique interpretation of shape and configuration coexistence at $N=27$ and 28 in the sulfur isotopic chain to the test. From an analysis of the electromagnetic transition strengths and quadrupole moments predicted within the shell model, it is shown that the onset of shape coexistence and the emergence of a simple collective structure appear suddenly in $^{43}\mathrm{S}$ with no indication of such patterns in the $N=27$ isotone $^{45}\mathrm{Ar}$.

In this paper, the isotonicity of the proximity operator and its applications are discussed. We first establish a few new conditions of the mappings such that their proximity operators are isotone with respect to orders induced different minihedral cones. Some properties and examples for these conditions are then introduced. We especially consider the isotonicity of the proximity operator with respect to one order induced by a subdual cone and two orders. To estimate the convergence rate of the iterative algorithms, some other inequality characterizations of the proximity operator with respect to the orders are then proved. As applications, some solvability and approximation theorems for the mixed variational inequality and optimization problems are established by order approaches, in which the mappings need not to be continuous and the solutions are optimal with respect to the orders. By using the isotonicity of the proximity operator with respect to two orders, we overcome the absence of the regularity of the order. The convergence rate of forward–backward algorithms is finally estimated by order approaches.

In topology, there are known results on preservation of the fixed point existence property under any homotopy of self-mappings on some spaces in the event that the initial mapping has a nonzero Lefschetz number. For contracting mappings of metric spaces and some of their generalizations, there are known results by M. Frigon on preservation of the contraction property and, consequently, the fixed point existence property under some special homotopies. In 1984, J.W.Walker introduced a discrete counterpart of homotopy for self-mappings of an ordered set, which he called an order isotone homotopy. The naturalness of this notion and its relation to the usual continuous homotopy follow from the work by R. E. Stong (1966). Recently, the author and D. A.Podoprikhin have extended Walker’s notion of an order isotone homotopy and suggested sufficient conditions for preservation of the fixed point (coincidence point) existence property under such discrete homotopy (a pair of homotopies) of a mapping (a pair of mappings) of ordered sets. This paper contains metric counterparts of the obtained results and some corollaries. The method of ordering a metric space proposed by A. Brondsted in 1974 is used.

Studying fuzzy attribute-oriented concept lattices has been a challenging issue of Formal Concept Analysis. In [19], the author introduced a fuzzy similarity relation between two collections of L-sets and proved some properties of this similarity type. In this paper, based on a duality technique which allowed us to transfer some properties from antitone to isotone fuzzy concept lattices, we provide alternative proofs for the inequality relations between the similarity of fuzzy attribute-oriented concept lattices and the similarity of the fuzzy contexts.

For bounded lattices L1 and L2, let $${f\colon L_1 \to L_2}$$ be a lattice homomorphism. Then the map $${{\rm Princ}(f)\colon \rm {Princ}(\it L_1) \to {\rm Princ}(\it L_2)}$$ , defined by $${{\rm con}(x,y) \mapsto {\rm con}(f(x),f(y))}$$ , is a 0-preserving isotone map from the bounded ordered set Princ(L1) of principal congruences of L1 to that of L2. We prove that every 0-preserving isotone map between two bounded ordered sets can be represented in this way. Our result generalizes a 2016 result of G. Gratzer from $${\{0,1}\}$$ -preserving isotone maps to 0-preserving isotone maps.

Resonance non-positone and non-isotone problems for first order differential systems subjected to non-local boundary conditions are reduced to the non-resonance positone and isotone case by changes of variables. This allows us to prove the existence of multiple positive solutions. The theory is illustrated by two examples for which three positive numerical solutions are obtained using the Mathematica shooting program.

The aim of this paper is to present a fuzzification of Tarski's fixed point theorem without the assumption of transitivity. For this purpose a new structure – the so called L-complete propelattice, which generalizes complete lattices and completely lattice L-ordered sets, is introduced. Our results show that for L-fuzzy isotone maps on L-complete propelattices a variant of Tarski's fixed point theorem holds. Especially, the set of fixed points is nonempty and of a certain structure.

We prove some nontrivial corollaries of the Schauder theorem. We use these corollaries to prove a theorem concerning the total preservation of solvability of a controlled functional operator equation of the Hammerstein type with non-isotone and non-majorizable operator component in the right-hand side. We illustrate the application of the abstract theory by the example of the Dirichlet problem associated with a semilinear elliptic equation similar to a stationary diffusionreaction equation.

The main idea of the paper is to generalize the concept of lattice valued fuzzy measures and integrals for data from complete residuated lattice where double negation law holds and then to show their relationship to isotone \({\mathcal L}\)-fuzzy concept forming operators.

7 pags., 4 figs., 1 tab., Excited states in the N=40 isotone Ti were populated via the V(p,2p)Ti reaction at ∼200 MeV/nucleon at the Radioactive Isotope Beam Factory and studied using γ-ray spectroscopy. The energies of the 2 →0 and 4 →2 transitions, observed here for the first time, indicate a deformed Ti ground state. These energies are increased compared to the neighboring Cr and Fe isotones, suggesting a small decrease of quadrupole collectivity. The present measurement is well reproduced by large-scale shell-model calculations based on effective interactions, while ab initio and beyond mean-field calculations do not yet reproduce our findings. The shell-model calculations for Ti show a dominant configuration with four neutrons excited across the N=40 gap. Likewise, they indicate that the N=40 island of inversion extends down to Z=20, disfavoring a possible doubly magic character of the elusive Ca., We thank the RIKEN Nishina Center accelerator staff and the Bi-gRIPS team for the stable operation of the high-intensity Zn beam and for the preparation of the secondary beam setting. K.O. ac-knowledges the support by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (JSPS) JP16K05352. A.P. is supported in part by the Ministerio de Ciencia, Innovación y Universidades (Spain), Severo Ochoa Programme SEV-2016-0597 and grant PGC-2018-94583. F.B. is supported by the RIKEN Spe-cial Postdoctoral Researcher Program. L.X.C. and B.D.L. would like to thank the Vietnam Ministry of Science and Technology (MOST) for its support through the Physics Development Program Grant No. ÐTÐLCN.25/18. I.G. has been supported by HIC for FAIR and Croatian Science Foundation under projects no. 1257 and 7194. D. So. was supported by the the European Regional Develop-ment Fund contract No. GINOP-2.3.3-15-2016-00034 and the National Research, Development and Innovation Fund of Hungary via Project No. K128947. V.V. acknowledges support from the Span-ish Ministerio de Economía y Competitividad under Contract No. FPA2017-84756-C4-2-P. K.I.H., D.K. and S.Y.P. acknowledge the sup-port from the National Research Foundation of Korea grant No. 2018R1A5A1025563 and 2019M7A1A1033186. The development of MINOS was supported by the European Research Council through the ERC Grant No. MINOS-258567. This work was also supported by the JSPS KAKENHI Grant No. 18K03639, MEXT as “Priority is-sue on post-K computer” (Elucidation of the fundamental laws and evolution of the universe), the Joint Institute for Computational Fundamental Science (JICFuS), the CNS-RIKEN joint project for large-scale nuclear structure calculations, Natural Sciences and Engineering Research Council (NSERC) of Canada, the Deutsche Forschungsgemeinschaft – Projektnummer 279384907 – SFB 1245, the PRISMA Cluster of Excellence, and the BMBF under Contracts No. 05P18RDFN1 and 05P19RDFN1. TRIUMF receives funding via a contribution through the National Research Council Canada. Com-putations were performed at the Jülich Supercomputing Center (JURECA)

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

The level structure in neutron-deficient nucleus 91Ru was investigated via the 58Ni (36Ar, 2p1n ) 91Ru reaction at a beam energy of 111 MeV. Charged particles, neutrons, and -rays were emitted in this reaction and detected by the DIAMANT CsI ball, Neutron Wall, and the EXOGAM Ge clover array, respectively. In addition to the previously reported levels in 91Ru, new low-to-medium spin states were observed. Angular correlation and linear polarization measurements were performed to unambiguously determine spins and parities of the excited states in 91Ru. The low-spin states of 91Ru exhibit a scheme of multi-quasiparticle excitations, which is very similar to that of the neighboring isotone. These excitations have been interpreted in terms of the shell model. The calculations performed in the configuration space reproduce the experimental excitation energies reasonably well, supporting the interpretation of the newly assigned positive-parity states in terms of the three quasiparticle configurations and .

The heaviest $N$ = 127 even-odd isotone $^{219}\mathrm{U}$ was produced in a fusion evaporation reaction employing $^{40}\mathrm{Ar}$ ions bombarding $^{183}\mathrm{W}$ target. Fusion evaporation residues were separated in flight by the gas-filled recoil separator Spectrometer for Heavy Atoms and Nuclear Structure and subsequently identified using a recoil-$\ensuremath{\alpha}$ correlation method. The $\ensuremath{\alpha}$-decay properties of $^{219}\mathrm{U}$ were measured with improved precision, and two new $\ensuremath{\alpha}$-decay lines were observed and assigned as the decays from the ground state of $^{219}\mathrm{U}$ to the ($5/{2}^{\ensuremath{-}}$) and ($3/{2}^{\ensuremath{-}}$) states of $^{215}\mathrm{Th}$, respectively. The systematics for the $\ensuremath{\alpha}$ decay of the $N$ = 127 even-odd isotones as well as the low-lying nuclear structure of their $N$ = 125 daughter nuclei are discussed.

Determining the position of one- and two-proton dripline for isotone of N = 18, 20, and 22 has been studied through Modified Relativistic Mean Field (MRMF). The model exemplifies three impacts, namely isovector-isoscalar coupling, tensors, and electromagnetic exchange through five parameter set variations. The position of one- and two-proton dripline for the isotones is predicted by applying two methods, which are two-proton separation energy, and Fermi energy. The research shows that the prediction of one- and two-proton dripline for isotone of N = 18, and N = 20 is positioned at Z = 22 and Z = 26 consecutively. Then, the prediction of one- and two-proton dripline for isotone of N = 22 has two positions, Z = 26 and Z = 28. The calculation result indicates that the position prediction for isotone of N = 18, N = 20, and N = 22 is following the research result conducted by Nazarewicz with RMF+NLSH model [1]. Meanwhile, isovector-isoscalar coupling, tensors, and electromagnetic exchange do not affect massively for the position prediction of two-proton dripline. However, the three methods affect one-proton dripline.

A systematic study on α-decay half-life time, T α , of α-particle emission from a large number of deformed heavy and superheavy nuclei is presented. The calculations are employed in the framework of the density-dependent cluster model. The microscopic α-daughter nuclear interaction potential is calculated in the framework of the double-folding model with the realistic effective Michigan-three-Yukawa Reid nucleon–nucleon interaction. We study the neutron number variation of log T α and arranged different isotones at each neutron magic number according to their stability, in the sense that the more stable isotone corresponds to the lowest value of log T α . We found that the half-life time becomes minimum when the neutron or proton numbers of the corresponding daughter nucleus are magic. Moreover, the half-life time is maximum for parent nucleus with magicity. The nuclear stability is assumed to be proportional with the depth of the minimum value in log T α for the daughter nucleus or the height of its maximum value for the parent one. The neutron magic numbers predicted and confirmed from the present study are 126, 152, 162, 172, 184, 196, 202 and 212, most of them were deduced by other authors based on different methods.

We describe an extension of formal fuzzy concept analysis allowing a user to choose which attributes are viewed as positive and which are viewed as negative. The two sets are then handled using a combination of previously studied antitone concept-forming operators and isotone concept-forming operators, respectively. The two main outputs of formal concept analysis, namely concept lattices and attribute implications, in the setting of positive and negative attributes are presented. An analogy of the main theorem of concept lattices and a relationship between the new concept lattice and the previously studied concept lattices is showed. We introduce basic syntactic and semantic notions for attribute implications called fuzzy containment implications. We consider two settings, one where the sets of positive and negative attributes are crisp sets, and a generalization, where the two sets are fuzzy sets.

Fixed point theorems for G -isotone mappings, which extend some recent results for mixed monotone and isotone mappings in partially ordered metric spaces are proved. Moreover, the equivalence between unidimensional and multidimensional fixed point theorems is investigated.

One of the main problems in formal concept analysis (especially in fuzzy setting) is to reduce a concept lattice of a formal context to appropriate size to make it graspable and understandable. A natural way to do it is to substitute the formal context by its block relation which is equivalent to factorization of the concept lattice by a complete tolerance. We generalize known results on the correspondence of block relations of formal contexts and complete tolerances on concept lattices to fuzzy setting and we provide an illustrative example of using block relations to reduce the size of a concept lattice. We generalize known results on the correspondence of block relations and complete tolerances.We provide an illustrative example of using block relations to reduce the size of a concept lattice.We consider both, the antitone and the isotone case.

Algebraic characters of linguistic truth-valued lattice implication algebras (L-LIAs) are focused in this paper. Concretely, the concept of derivation coming from analytic theory is introduced in L-LIAs, and then some properties of derivations are given in L-LIAs. Subsequently, some special derivations (such as isotone deri-vation, embedding derivation, isomorphism derivation and regular derivation) are discussed in L-LIAs along with the relations among them. The relations between derivations and lattice implication homomorphisms are also investigated in L-LIAs. At the end, the derivations of some algebraic substructures are described in L-LIAs.

The main aim of this article is to study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under contraction mapping principle on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to an integral equation. The results we obtain generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

Exploiting the concept of the dinuclear system, the interaction potential energy of two fragments that are quite close to each other is analyzed. A semi-classical method is used to calculate fission fragment yields using a simplified two-dimensional scission-point model. By considering the tip-to-tip orientation at the scission point of the fission process, we investigate the mass, charge, and kinetic-energy distributions of the fission fragments, for excitation energies in the 0-20 MeV range. Our results show that the fission fragment distributions are reproduced quite well, including the recent experimental results for the isotone chain [D Ramos et al. Phys. Rev. C 97, 054612 (2018)]. Thus, the simplified model is useful for multi-parameter global measurements of fission products.

The paper is devoted to the problem of the existence of common fixed points and coincidence points of a family of set-valued maps of ordered sets. Fixed-point and coincidence theorems for families of set-values maps are presented, which generalize some of the known results. The presented theorems, unlike previous ones, do not assume the maps to be isotone or coverable. They require only the existence of special chains having lower bounds with certain properties in the ordered set.

In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples.