DETERMINING THE LOCATION OF AN UNMANNED AERIAL VEHICLE BASED ON VIDEO CAMERA IMAGES

The paper deals with the problem of determining the location of an unmanned aerial vehicle from video and photo images taken by surveillance cameras. As the observation area is considered to be sufficiently limited, the area under consideration can be taken as part of a plane. The solution to the problem is based on the construction of a bijective mapping between the known geographic coordinates of three different objects recognized in the images and their coordinates relative to the monitor plane. To this end, the geographical coordinates of the objects (latitude and longitude) are first converted to the Mercator projection, and a bijective mapping is built between the coordinates of the objects calculated in the Mercator projection and the coordinates relative to the camera monitor plane. Then, based on the current orientation angles of the unmanned aerial vehicle, the coordinates of the projection of its position on the monitor plane are calculated, and the geographical coordinates are found by applying the inverse of the constructed bijective mapping.

Even-odd Harmonious Labeling of Some Graphs

Let G = be a graph, with and . An injective mapping is called an even-odd harmonious labeling of the graph G, if an induced edge mapping such that (i) is bijective mapping (ii) The graph acquired from this labeling is called even-odd harmonious graph. In this paper, we discovered some interesting results like H-graph, comb graph, bistar graph and graph for even-odd harmonious labeling.

Mappings preserving sum of products a∘b+ba∗ on factor von Neumann algebras

Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping Φ:A→B satisfies Φ(a∘b+ba∗)=Φ(a)∘Φ(b)+Φ(b)Φ(a)∗ (where ∘ is the special Jordan product on A and B, respectively), for all elements a,b∈A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism.

Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains

This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains.

Edge δ− Graceful Labeling for Some Cyclic-Related Graphs

In this paper, we introduce a new type of labeling of a graph G with p vertices and q edges called edge δ− graceful labeling, for any positive integer δ, as a bijective mapping f of the edge set EG into the set δ,2δ,3δ,⋯,qδ such that the induced mapping f∗:VG→0,δ,2δ,3δ,⋯,qδ−δ, given by f∗u=∑uv∈EGfuvmodδk, where k=maxp,q, is an injective function. We prove the existence of an edge δ− graceful labeling, for any positive integer δ, for some cycle-related graphs like the wheel graph, alternate triangular cycle, double wheel graph Wn,n, the prism graph Πn, the prism of the wheel PWn, the gear graph Gn, the closed helm CHn, the butterfly graph Bn, and the friendship Frn.

Ooid growth: Uniqueness of time-invariant, smooth shapes in 2D

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping, we demonstrate that the steady parameters associated with the physical environment determine a unique, time-invariant, compact shape among smooth, convex curves embedded in ℝ2. It is also revealed that any time-invariant solution possesses D2 symmetry. The model predictions remarkably agree with ooid shapes observed in nature.

Methods and Algorithms for Pseudo-probabilistic Encryption with Shared Key

As a method for providing security of the messages sent via a public channel in the case of potential coercive attacks there had been proposed algorithms and protocols of deniable encryption. The lasts are divided on the following types: 1) schemes with public key, 2) schemes with shares secret key, and 3) no-key schemes. There are introduced pseudo-probabilistic symmetric ciphers that represent a particular variant of implementing deniable encryption algorithms. It is discussed application of the pseudo-probabilistic encryption for constructing special mechanisms of the information protection including steganographic channels hidden in ciphertexts. There are considered methods for designing stream and block pseudo-probabilistic encryption algorithms that implement simultaneous ciphering fake and secret messages so that the generated ciphertext is computationally indistinguishable from the ciphertext obtained as output of the probabilistic encryption of the fake message. The requirement of the ciphertext indistinguishability from the probabilistic encryption has been used as one of the design criteria. To implement this criterion in the construction scheme of the pseudo-probabilistic ciphers it is included step of bijective mapping pairs of intermediate ciphertext blocks of the fake and secret messages into a single expanded block of the output ciphertext. Implementations of the pseudo-probabilistic block ciphers in which algorithms for recovering the fake and secret messages coincide completely are also considered. There are proposed general approaches to constructing no-key encryption protocols and randomized pseudo-probabilistic block ciphers. Concrete implementations of the cryptoschemes of such types are presented.

All or Nothing at All

We continue a study of unconditionally secure all-or-nothing transforms (AONT) begun by Stinson (2001). An AONT is a bijective mapping that constructs $s$ outputs from $s$ inputs. We consider the security of $t$ inputs, when $s-t$ outputs are known. Previous work concerned the case $t=1$; here we consider the problem for general $t$, focussing on the case $t=2$. We investigate constructions of binary matrices for which the desired properties hold with the maximum probability. Upper bounds on these probabilities are obtained via a quadratic programming approach, while lower bounds can be obtained from combinatorial constructions based on symmetric BIBDs and cyclotomy. We also report some results on exhaustive searches and random constructions for small values of $s$.