The zeros off(z) = (az - b)^{n} pm (cz - d)^{n}are found to lie on a circle of radius|(ad - cb)/(|a|^{2} - |c|^{2})|with its center atz = (a^{ast}b - c^{ast}d)/(|a|^{2} - |c|^{2}), wherea, b, c, anddare complex numbers andnis assumed real. When|a| = |c|the locus of the zeros is a straight line perpendicular to the line joining the pointsb/aandb/cand intersecting it atz = 0.5(b/a + d/c). The zeros are found analytically and constructed geometrically. 相似文献
Valiant [L. Valiant, Completeness classes in algebra, in: Proc. 11th Annual ACM Symposium on the Theory of Computing, Atlanta, GA, 1979, pp. 249–261] proved that every polynomial of formula size e is a projection of the (e+2)×(e+2) determinant polynomial. We improve “e+2” to “e+1”, also for a definition of formula size that does not count multiplications by constants as gates. Our proof imitates the “2e+2” proof of von zur Gathen [J. von zur Gathen, Feasible arithmetic computations: Valiant's hypothesis, Journal of Symbolic Computation 4 (1987) 137–172], but uses different invariants and a tighter set of base cases. 相似文献
This paper introduces a novel lossless binary data compression scheme that is based on the error correcting Hamming codes, namely the HCDC scheme. In this scheme, the binary sequence to be compressed is divided into blocks of n bits length. To utilize the Hamming codes, the block is considered as a Hamming codeword that consists of p parity bits and d data bits (n=d+p). Then each block is tested to find if it is a valid or a non-valid Hamming codeword. For a valid block, only the d data bits preceded by 1 are written to the compressed file, while for a non-valid block all n bits preceded by 0 are written to the compressed file. These additional 1 and 0 bits are used to distinguish the valid and the non-valid blocks during the decompression process. An analytical formula is derived for computing the compression ratio as a function of block size, and fraction of valid data blocks in the sequence. The performance of the HCDC scheme is analyzed, and the results obtained are presented in tables and graphs. Finally, conclusions and recommendations for future works are pointed out. 相似文献
The cover image is based on the Research Article High‐gain nonlinear observer‐based impedance control for deformable object cooperative teleoperation with nonlinear contact model by Zhenyu Lu et al., https://doi.org/10.1002/rnc.4880 .
For each nonempty binary word w=c1c2cq, where ci{0,1}, the nonnegative integer ∑i=1q (q+1−i)ci is called the moment of w and is denoted by M(w). Let [w] denote the conjugacy class of w. Define M([w])={M(u): u[w]}, N(w)={M(u)−M(w): u[w]} and δ(w)=max{M(u)−M(v): u,v[w]}. Using these objects, we obtain equivalent conditions for a binary word to be an -word (respectively, a power of an -word). For instance, we prove that the following statements are equivalent for any binary word w with |w|2: (a) w is an -word, (b) δ(w)=|w|−1, (c) w is a cyclic balanced primitive word, (d) M([w]) is a set of |w| consecutive positive integers, (e) N(w) is a set of |w| consecutive integers and 0N(w), (f) w is primitive and [w]St. 相似文献
This paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a β-contractive ellipsoidal set , the key idea is to construct a polyhedral set that lies between the ellipsoidal sets and . A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired polyhedral set. The problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs. 相似文献
Embedding of paths have attracted much attention in the parallel processing. Many-to-many communication is one of the most central issues in various interconnection networks. A graph G is globally two-equal-disjoint path coverable if for any two distinct pairs of vertices (u,v) and (w,x) of G, there exist two disjoint paths P and Q satisfied that (1) P (Q, respectively) joins u and v (w and x, respectively), (2) |P|=|Q|, and (3) V(PQ)=V(G). The Matching Composition Network (MCN) is a family of networks which two components are connected by a perfect matching. In this paper, we consider the globally two-equal-disjoint path cover property of MCN. Applying our result, the Crossed cube CQn, the Twisted cube TQn, and the Möbius cube MQn can all be proven to be globally two-equal-disjoint path coverable for n5. 相似文献
We propose a method to quantify the complexity of conditional probability measures by a Hilbert space seminorm of the logarithm of its density. The concept of reproducing kernel Hilbert spaces (RKHSs) is a flexible tool to define such a seminorm by choosing an appropriate kernel. We present several examples with artificial data sets where our kernel-based complexity measure is consistent with our intuitive understanding of complexity of densities.
The intention behind the complexity measure is to provide a new approach to inferring causal directions. The idea is that the factorization of the joint probability measure P(effect,cause) into P(effect|cause)P(cause) leads typically to “simpler” and “smoother” terms than the factorization into P(cause|effect)P(effect). Since the conventional constraint-based approach of causal discovery is not able to determine the causal direction between only two variables, our inference principle can in particular be useful when combined with other existing methods.
We provide several simple examples with real-world data where the true causal directions indeed lead to simpler (conditional) densities. 相似文献
We give a framework for developing the least model semantics, fixpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ) and some classical first-order Horn clauses. Our approach is direct and no special restriction on occurrences of □i and i is required. We apply our framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4, 5 (in the form, e.g. 4:□i→□j□k) and I:□i→□j. Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more efficient. 相似文献
In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain,
where f:[t1,σ(t2)]×[0,∞)×R→[0,∞) is continuous and p:[t1,σ(t2)]→[0,∞) a nonnegative function that is allowed to vanish on some subintervals of [t1,σ(t2)] of the measure chain. The method involves applications of a new fixed-point theorem due to Bai and Ge [Z.B. Bai, W.G. Ge, Existence of three positive solutions for some second order boundary-value problems, Comput. Math. Appl. 48 (2004) 699–707]. The emphasis is put on the nonlinear term f involved with the first order delta derivative xΔ(t). 相似文献