R-trees and related structures, like R-trees and R-trees, have been used to answer queries involving topological information about objects represented by their minimum bounding rectangles (MBRs). This paper describes how the R-tree method can be used for the storage and retrieval of direction relations. Direction relations deal with order in space, as for instance, left, above, north, southeast...

Let M be a vector space over a field k and R ∈ End k(M ⊗ M). This paper studies what shall be called the Long equation: that is, the system of nonlinear equations R12R13 = R13R12 and R12R23 = R23R12 in End k(M ⊗ M ⊗ M). Any symmetric solution of this system supplies us a solution of the integrability condition of the Knizhnik-Zamolodchikov equation: [R12, R13+R23] = 0 ([4] or [10]). We shall ap...

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

We begin with establishing properties of the unit revenue function, g(·). Lemma 6. 1. g(·) is a non-negative, continuous, non-decreasing, and concave function on R+, with g(0) = 0. 2. yg(1/y) is non-decreasing and concave on R++. 3. g(y)/y is non-increasing on R+. 4. If u, v > 0, then g(u) g(v) ≥ min( u v , 1), 1 u ∫ u 0 g(v)dv ≤ g(u/2). Proof. 1. That g(·) is non-negative, continuous and non-d...

The R-Tree and variant indexes have been used for multidimensional indexing since 1984 and applied to temporal data since 1994. Despite this, there are few functional implementations of the index that can be applied directly to the temporal data. This paper explores the use of the index for temporal subsequence searches and identifies two implications that must be considered so the index can be...

in this study, the effect of the secondary structure of the protein on the acid strength of three structures of random (r), alpha helix (α) and beta sheet (b) were investigated theoretically. these structures are related to the cationic amino acids of histidine and lysine in the polypeptide chain of eight-glycine residue. computational methods at the hf, b3lyp, x3lyp and m05-2x levels in the ga...

in this paper, a new approach for solving the second order fuzzy differential equations (fde) with fuzzy initial value, under strongly generalized h-differentiability is presented. solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...

We show the closed-form solution to the maximization of tr(A R), where A is given and R is unknown rotation matrix. This problem occurs in many computer vision tasks involving optimal rotation matrix estimation. The solution has been continuously reinvented in different fields as part of specific problems. We summarize the historical evolution of the problem and present the general proof of the...

The system of equations studied in this paper is —Au—gXu) on R, d^2, with w R ^ R " and g(u) = dG/dui. Associated with this system is the action, S(u) = J {i|Fw|G(u)}. Under appropriate conditions on G (which differ for d = 2 and d_-3) it is proved that the system has a solution, wφO, of finite action and that this solution also minimizes the action within the class {v is a solution, v has fini...