Narrow Results

Transfer reliability has an important impact on the urban bus network. The proportion of zero and one transfer time is a key indicator to measure the connectivity of bus networks. However, it is hard to calculate the transfer time between nodes because of the complicated network structure. In this paper, the topological structures of urban bus network in Jinan are constructed by space L and space P. A method to calculate transfer times between stations has been proposed by reachable matrix under space P. The result shows that it is efficient to calculate the transfer time between nodes in large networks. In order to test the transfer reliability, a node failure process has been built according to degree, clustering coefficient and betweenness centrality under space L and space P. The results show that the deliberate attack by betweenness centrality under space P is more effective compared with other five attack modes. This research could provide a power tool to find hub stations in bus networks and give a help for traffic manager to guarantee the normal operation of urban bus systems.

We define a kind of simple actions of labelled transition systems. These actions cannot be atomic; consequently, their compositions cannot be inductive. Their informal meaning is that in one simple action we can suppose the maximum of its modifications. Such actions are called hybrid. Then we propose two formal theories on hybrid actions (the hybrid actions are defined there as non-well-founded terms and non-well-founded formulas): group theory and Boolean algebra. Both theories possess many unusual properties such as the following one: the same member of this group theory behaves as multiplicative zero in respect to one members and as multiplicative unit in respect to other members.

The demand for high performance, low power/secured handheld equipment increased the need for high speed/low energy and efficient encryption/decryption algorithms. Recently, efficient techniques were suggested to increase the standard of security as well as the speed of portable and handheld devices. Also, those techniques cause increment in the lifetime of battery by reducing the total silicon capacitance and minimizing the switching activity. This paper presents two approaches to reduce the number of logic gates at S7 and S9 of MISTY1 in order to reduce the total delay time, power dissipation and silicon area. The Logic Gate Reduction Approach (LGRA) reduces the number of logic gates by applying Boolean Algebra rules and simplifications, while the Duplicated Gate Reduction Approach (DGRA) removes the redundant XOR and AND logic gates which form the S7 and S9 blocks ciphers. The LGRA approach shows that the throughput enhanced by 21.1% compared to the conventional design, the silicon area reduced by 26.8%, while the dynamic power dissipation is reduced by 21.7% on average. The DGRA approach shows that the throughput enhanced by 3.8% compared to the conventional design, the silicon area reduced by 31.7%, while the dynamic power dissipation is reduced by 27% on average. As a result, the proposed approaches could be fit for next generation of handheld and portable devices.

In the Constructive Solid Geometry (CSG) representation a geometric object is described as the hierarchical combination of a number of primitive shapes using the operations union, intersection, subtraction, and exclusive-union. This hierarchical description defines an expression tree, T, called the CSG tree, with leaves associated with primitive shapes, internal nodes associated with operations, and whose "value" is the geometric object. Evaluation of CSG trees is an important computation that arises in many rendering and analysis problems for geometric models, with ray shooting (also known as "ray casting") being one of the most important. Given any CSG tree T, which may be unbalanced, we show how to convert T into a functionally-equivalent binary tree, D, that is balanced. We demonstrate the utility of this conversion by showing how it can be used to improve the worst-case running time for ray shooting against a CSG model from O(n²) to O(n log n), which is optimal. In addition, the practicality of our method has been demonstrated in experimental benchmarking tests using the BRL-CAD package.

It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like structures over the unit interval of real numbers, can be obtained without the assumption of statistical independence of input empirical data charged with uncertainty.

Starting with the zero-square "zeon algebra," the regular representation gives rise to a Boolean lattice representation of sl(2). We detail the su(2) content of the Boolean lattice, providing the irreducible representations carried by the algebra generated by the subsets of an n-set. The group elements are found, exhibiting the "special functions" in this context. The corresponding Leibniz rule and group law are shown. Krawtchouk polynomials, the Hamming and the Johnson schemes appear naturally. Applications to the Boolean poset and the structure of Hadamard–Sylvester matrices are shown as well.

Anti-elementarity is a strong way of ensuring that a class of structures, in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form ${ℒ}_{\infty \lambda }$. We prove that many naturally defined classes are anti-elementary, including the following:

• the class of all lattices of finitely generated convex $\ell$-subgroups of members of any class of $\ell$-groups containing all Archimedean $\ell$-groups;
• the class of all semilattices of finitely generated $\ell$-ideals of members of any nontrivial quasivariety of $\ell$-groups;
• the class of all Stone duals of spectra of MV-algebras — this yields a negative solution to the MV-spectrum Problem;
• the class of all semilattices of finitely generated two-sided ideals of rings;
• the class of all semilattices of finitely generated submodules of modules;
• the class of all monoids encoding the nonstable K₀-theory of von Neumann regular rings, respectively, C*-algebras of real rank zero;
• (assuming arbitrarily large Erdős cardinals) the class of all coordinatizable sectionally complemented modular lattices with a large $4$-frame.

The main underlying principle is that under quite general conditions, for a functor $\mathrm{\Phi }:{𝒜}\to {ℬ}$, if there exists a noncommutative diagram $\overrightarrow{D}$ of ${𝒜}$, indexed by a common sort of poset called an almost join-semilattice, such that

• $\mathrm{\Phi }{\overrightarrow{D}}^I$ is a commutative diagram for every set $I$,
• $\mathrm{\Phi }\overrightarrow{D}\ncong \mathrm{\Phi }\overrightarrow{X}$ for any commutative diagram $\overrightarrow{X}$ in ${𝒜}$,

then the range of $\mathrm{\Phi }$ is anti-elementary.

We characterize measure spaces such that the canonical map $L_{\infty }\to L_1^{\ast }$ is surjective. In case of $d$-dimensional Hausdorff measure on a complete separable metric space $X$, we give two equivalent conditions. We give examples of $X$ and $d$ so that whether these conditions are met is undecidable in ZFC, including one with $d$ equals the Hausdorff dimension of $X$.

We show in this note that if $B$ is a Boolean subalgebra of the lattice quantum logic $L$, then each state on $B$ can be extended over $L$ as a Jauch–Piron state provided $L$ is Jauch–Piron unital with respect to $B$ (i.e. for each nonzero $b\in B$, there is a Jauch–Piron state $s$ on $L$ such that $s(b)=1$). We then discuss this result for the case of $L$ being the Hilbert space logic $L(H)$ and $L$ being a set-representable logic.

We parameterize countable locally standard Boolean measure algebras by pairs of a Steinitz number and a real number greater or equal to $1.$ This is an analog of the theorems of Dixmier and Baranov.

This paper is a continuation of our previous work [10]. By GAERS-1, we denote the class of generalized abelian exchange rings with stable range 1. In this paper, we first prove that for any ring R ∈ GAERS-1 and any ideal I of R, K₀(R/I) is an archimedean ℓ-group, which is a natural generalization of [10, Theorem 5.3]. As applications, we establish explicit characterizations for the K₀-simplicity of such rings in the sense of [3], and investigate the norm completeness of their K₀-groups. Finally, we characterize the primitive idempotents in R by K₀(R) with ordered structure, from which we can further determine completely the structure of K₀(R).

We investigate subadditive measures on orthomodular lattices. We show as the main result that the Boolean algebra, the special metric orthomodular lattice and the orthomodular lattice which is unital with respect to subadditive states are equivalent. This result may find an application in the foundation of quantum theories and mathematical logic.

Given a complete residuated lattice ${ℒ}:=(L;\wedge ,\vee ,\ominus ,\twoheadrightarrow ,⊸;0,1)$ and a mono-unary algebra ${𝒜}:=(A;f)$, it is well known that ${ℒ}$ and the residuated lattice ${ℱ}u(A,L):=(\mathrm{\text{Fu}}(A,L);\wedge ,\vee ,\ominus ,\twoheadrightarrow ,⊸;\underline{0},\underline{1})$ of $L$-fuzzy subsets of $A$ satisfy the same residuated lattice identities. In this paper, we show that ${ℒ}$ and the residuated lattice ${ℱ}s({𝒜},L):=(\mathrm{\text{Fs}}({𝒜},L);\wedge ,\vee ,\ominus ,\hookrightarrow ,\looparrowright ;\underline{0},\underline{1})$ of $L$-fuzzy subalgebras of ${𝒜}$ satisfy the same residuated lattice identities if and only if the Heyting algebra ${𝒮}ub({𝒜}):=(\mathrm{\text{Sub}}({𝒜});\cap ,\cup ,\Rightarrow ;\varnothing ,A)$ of subuniverses of ${𝒜}$ is a Boolean algebra. We also show that ${ℱ}s({𝒜},L)$ is a Boolean algebra (respectively, an $MV$-algebra) if and only if ${ℒ}$ is a Boolean algebra (respectively, an $MV$-algebra) and ${𝒮}ub({𝒜})$ is a Boolean algebra.

In this paper, we defined the concepts of $(\wedge ,\odot )$-derivation and $(\to ,\vee )$-derivation for $BL$-algebras and discuss some related results. We study the connection between these derivations on an $BL$-algebra $A$. Also we study these derivations on Boolean center $B(A)$, $MV$ center, Godel center of a $BL$-algebra $A$.

In this paper, we defined the concepts of $(\wedge ,\odot )$-derivation and $(\to ,\vee )$-derivation for $BL$-algebras and discuss some related results. We study the connection between these derivations on an $BL$-algebra $A$. Also, we study these derivations on Boolean center $B(A)$, $MV$ center, Godel center of a $BL$-algebra $A$.

The concept of a pseudo-complementation on a Generalized Almost Distributive Lattice (GADL) with 0 is introduced and proved that there is a one-to-one correspondence between the pseudo-complementations on a GADL L with 0 and left identity elements of L. The concept of *–GADL, disjunctive GADL is also introduced. We characterized *–GADL in terms of disjunctive GADL.

The concept of annihilator ideals is introduced in C-algebras. Some properties of these annihilator ideals are studied and then proved that the class of all annihilator ideals forms a complete Boolean algebra. A set of equivalent conditions are obtained for every ideal of a C-algebra to become an annihilator ideal. Some properties of homomorphic images and inverse images of annihilators ideals of a C-algebra are studied.

Characterized Quasi-complemented Almost Distributive Lattice (ADL) in terms of dominator ideals. By using the closure operator on the set of all ideals of an ADL introduced the concept of closure ideals and studied their important results. Finally, the class of all closure ideals of ADL are isomorphic to the class of all ideals of .

The notion of Stonity of a pseudo-complemented Almost Distributive Lattice A is introduced and several properties of the Stonity S(A) of A are proved. Mainly, it is proved that the Stonity S(A) is the largest sub-ADL of A which is a Stone ADL and that S(A) is independent of the pseudo-complementation on A.

We prove that for any Boolean space $X$ and a dense Almost Distributive Lattice (ADL) $D$ with a maximal element, the set ${𝒞}(X,D)$ of all continuous functions of $X$ into the discrete $D$ is a Stone ADL. Conversely, it is proved that any Stone ADL is a homomorphic image of ${𝒞}(X,D)$ for a suitable Boolean space $X$ and a dense ADL $D$ with a maximal element.