(T ε ≤ K ≤ T ) are considered, where αj = |ρj(1)| (coshπκj) , and ρj(1) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λj = κ 2 j + 1 4 to which the Hecke series Hj(s) is attached. The problem is transformed to the estimation of a classical exponential sum involving the binary additive divisor problem. The analogous exponential sums with Hj( 1 2 ) or H j...

The following problem is considered in this paper : maxx∈D{∑mj=1 gj(x)/hj(x)}, where gj(x) ≥ 0 and hj(x) > 0, j = 1, · · · , m are d.c. (difference of convex) functions over a convex compact set D in R. Specifically, it is reformulated into the problem of maximizing a linear objective function over a feasible region defined by multiple reverse convex functions. Several favorable properties are ...

This paper addresses the distributed optimal decoupling synchronous control of multiple autonomous unmanned linear systems (MAUS) subject to complex network dynamic coupling. The leader–follower mechanism based on neighborhood error dynamics is established and coupling term regarded as external disturbance realize cooperative each agent. Bounded L2-Gain problem for formulated into a multi-playe...

Let P be complex projective space of dimension m, π : Cm+1\{0} → P the standard projection and M ⊂ P a closed subset (with respect to the usual topology of a real manifold of dimension 2m). A hypersurface in P is the projection of the set of zeros of a non-constant homogeneous form in m+ 1 variables. Let n be a positive integer. Consider a set of hypersurfaces {Hj} j=1 with the property M ∩ ⋂...

Handling an Update: When an update (it, ct) arrives, then ct is added to one entry in each row of the array count. Specifically, ∀1 ≤ j ≤ d, count [j, hj(it)]← count [j, hj(it)] + ct. Lemma 1. The space used by Count-Min Sketch is O(wd) ≡ O( ln 1 δ ) words. Specifically, it uses an array which takes wd words and d hash functions, each of which can be stored using 2 words. An update can be handl...

We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex only depends on the spatial gradient solution. To be specific, we prove that under certain assumptions, two proposed represent to sets HJ PDEs with zero error. also implement our using Tensorflow provide...

1 Department of Biology, Faculty of Science, Kobe University, Rokkodai 1-1, Nada-ku, Kobe, 657-8501, Japan 2 Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST), Chuou-ku, Tokyo, 113-0027, Japan 3 Department of Chemistry, Pohang University of Science and Technology, San 31 Hyoja Dong, Pohang 790-784, Korea 4 Department of Life Science, Graduat...

Freight transportation has increased very rapidly in the Republic of Korea owing to economic growth and expanding international trade. However, the freight transport sector in the Republic of Korea has been regarded as inefficient and the inefficiencies can be attributed to many factors, including an outdated regulatory framework, business practices and a lack of proper infrastructure. Since fr...

We utilize radial basis functions (RBFs) to construct numerical schemes for Hamilton–Jacobi (HJ) equations on unstructured data sets in arbitrary dimensions. The computational setup is a meshless discretization of the physical domain. We derive monotone schemes on unstructured data sets to compute the viscosity solutions. The essentially nonoscillatory (ENO) mechanism is combined with radial ba...

We study algorithms simulating a system evolving with Hamiltonian H = Pm j=1Hj , where each of the Hj , j = 1, . . . ,m, can be simulated efficiently. We are interested in the cost for approximating e−iHt, t ∈ R, with error ε. We consider algorithms based on high order splitting formulas that play an important role in quantum Hamiltonian simulation. These formulas approximate e−iHt by a product...