<abstract><title style='display:none'>ABSTRACT</title>The k-nearest neighbour kernel density estimationmethod is a special type of the kernel density estimation method with the local choice of the bandwidth. An advantage of this estimator is that smoothing varies according to the number of observations in a particular region. The crucial problem is how to estimate the value of the parameter k. In the paper we discuss the problem of choosing the parameter k in a way that minimizes the value of the asymptotic mean integrated square error (AMISE). We define the class of the modified cosine densities that meet the requirements given by the AMISE. The results are compared in a simulation study.</abstract>

K-nearest neighbour kernel density estimation, the choice of optimal k

<abstract><title style='display:none'>Abstract</title> In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model</abstract>

Estimating the Short Rate from the Term Structures in the Vasicek Model

<abstract><title style='display:none'>Abstract</title>This article deals with the damaged and incomplete Old Babylonian tablet <italic>Plimpton 322</italic> which contains 4 columns and 15 rows of a cuneiform mathematical text. It has been shown that the presumed original table with its 7 columns and 39 rows represented: a table of square roots of numbers from 0 to 2 for mathematicians; an earliest rudiments of a trigonometric table for builders and surveyors where angles are not measured as an arc in a unit circle but as a side of a unit right-angled triangle; a list of the 39 exercises on reciprocal pairs, unit and integer-side right triangles (rectangles), factorization and square numbers for teachers.The article provides new arguments in favor of old disputes (squares of diagonals or widths; mistakes in previous analysis of errors in <italic>P322</italic>). Contradictory ideas about <italic>P322</italic> are discussed: Is it the table of triangle sides or factorization terms? Was it compiled by a parallel or independent factorization of the sides or of their squares? Are sides of an initial unit triangle enlarged or reduced by such a factorization? Does it contain two or four arithmetical errors?Time and dimensional requirements for calculation and writing of the complete tablet have been also estimated.</abstract>

<italic>Plimpton 322</italic> : A Universal Cuneiform Table for Old Babylonian Mathematicians, Builders, Surveyors and Teachers

<abstract><title style='display:none'>ABSTRACT</title>We describe the background of the Zodiac killer’s cipher, and present a strategy for how to attack the unsolved Z340 cipher. We present evidence that there is a high degree of non-randomness in the sequence of ciphertext symbols in this cipher, suggesting it has been constructed in a systematic way. Next, we use this information to design a tool for solving the Zodiac ciphers. Using this tool we are able to re-solve the known Z408 cipher.</abstract>

Department of Informatics, University of Bergen, N–5020 Bergen, NORWAY

Department of Applied Informatics, Information Technology, Slovak University of Technology, Ilkoviˇcova 3, SK–812-19 Bratislava, SLOVAKIA

The zodiac killer ciphers

<abstract><title style='display:none'>Abstract</title> We discuss some basic ideas and survey some fundamental constructions related to measure (a real-valued map the domain of which is a set of measurable objects carrying a suitable structure and the map partially preserves the structure): continuity, measurability, duality, extension. We show that in the category <italic>ID </italic>of difference posets of fuzzy sets and sequentially continuous difference-homomorphisms these constructions are intrinsic. Further, basic notions of the probability theory have natural generalizations within <italic>ID</italic>.</abstract>

Measures: continuity, measurability, duality, extension

<abstract><title style='display:none'>ABSTRACT</title> In this paper there are given problems from the Unsolved Problems Section on the homepage of the journal Uniform Distribution Theory &lt;http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf&gt; It contains 38 items and 5 overviews collected by the author and by Editors of UDT. They are focused at uniform distribution theory, more accurate, distri- bution functions of sequences, logarithm of primes, Euler totient function, van der Corput sequence, ratio sequences, set of integers of positive density, exponen- tial sequences, moment problems, Benford’s law, Gauss-Kuzmin theorem, Duffin- Schaeffer conjecture, extremes fQ fQ F(x,y)dg(x,y) over copulas g(x,y), sum- -of-digits sequence, etc. Some of them inspired new research activities. The aim of this printed version is publicity. </abstract>

UNSOLVED PROBLEMS

<abstract>
<title style='display:none'>Abstract</title>
In this article, an application of <italic>φ</italic>-metric is given via a geometrical example to show how it can help to measure distance for non-planar surfaces where the classical metric becomes incapable. We also introduce the concept of best proximity point and proximal contraction for a class of mappings in a <italic>φ</italic>-metric space and prove a best proximity point theorem for such class of contraction mappings from which the famous “Wardowski’s fixed point theorem” can be deduced as a particular case. To support our theorem, we provide an example in which Wardowski’s metric fixed point theorem cannot be applied.
</abstract>

An Application of <italic>φ</italic>-Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

<abstract>
<title style='display:none'>Abstract</title>
The initialization of the <italic>Strumok</italic> cipher is analyzed in this paper. A modified cipher initialization procedure is constructed for the <italic>Strumok-512</italic> cipher, which allows to show that the cipher initialization is not injective. Security against slide attacks is proved. Furthermore, the Guess-and-Determine attack on the <italic>Strumok-512</italic> cipher is constructed with complexity 2448.
</abstract>

Cryptanalysis of Strumok Cipher Initialization

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we are concerned with an iterative differential inclusion governed by the time-dependent maximal monotone operator with perturbation. The approach to solve our problem is based on the Yosida approximation technique. The theoretical result is applied to prove an existence result for a Lagrange optimal control problem without assumptions concerning convexity.
</abstract>

On a Non-Convex Lagrange Optimal Control Problem

<abstract>
<title style='display:none'>Abstract</title>
This paper investigates a fixed point over a complete b-metric space for a family of contractive mappings. In this paper, we have discovered new results in the direction of the complete b-metric space by using Rus contraction. Furthermore, we establish a common fixed point theorem between two mappings over complete b-metric space. We also provide some non-trivial examples to display the authenticity of our established results.
</abstract>

New Fixed Point Theorems on Complete <italic>b</italic>-Metric Space by Using Rus Contraction Mapping

<abstract>
<title style='display:none'>Abstract</title>
In this article, some under-appreciated characteristics of strongly star-Rothberger subsets are explored. Additionally, with the aid of the SSI property and MSSI property, semi-Rothberger and star semi-Rothberger spaces are represented by families of closed sets. Finally, several selection principle like attributes are produced that can reflect the previously mentioned sequential covering features in an inverted form.
</abstract>

Some Alternative Interpretations of Strongly Star Semi-Rothberger and Related Spaces

<abstract>
<title style='display:none'>Abstract</title>
We define and study a Banach-space-valued Nemytskiĭ operator and we find vector measure solutions for associated non-linear initial value problems.
</abstract>

The Nemytskiĭ Operator and Vector Measure Solutions for Non-Linear Initial Value Problems

<abstract><title style='display:none'>ABSTRACT</title>Random number generators represent one of basic cryptographic primitives used in creating cryptographic protocols. Their security evaluation represents very important part in the design, implementation and employment phase of the generator. One of important security requirements is the existence of a mathematical model describing the physical noise source and the statistical properties of the digitized noise derived from it. The aim of this paper is to propose the model of a class of generators using two jittery clocks with rationally related frequencies. The clock signals with related frequencies can be obtained using phase-locked loops, delay-locked loops or ring oscillators with adjusted oscillation periods. The proposed mathematical model is used to provide entropy per bit estimators and expected bias on the generated sequence. The model is validated by hardware experiments.</abstract>

Mathematical model of physical RNGs based on coherent sampling

<abstract><title style='display:none'>Abstract</title> Symmetric block ciphers are the most widely used cryptographic primitives. In addition to providing privacy, block ciphers are used as basic components in the construction of hash functions, message authentication codes, pseudorandom number generators, as a part of various cryptographic protocols, etc. Nowadays the most popular block cipher is AES (Advanced Encryption Standard). It is used as a standard of symmetric encryption in many countries. Several years ago it was found a theoretical attack exploiting the AES key expansion algorithm that allows reducing significantly the complexity comparing to the brute force attack. This article presents an advanced method of finding the number of active substitutions that helps to estimate the security of encryption algorithms against related-key attacks. The method was applied to a prospective block cipher, which is a candidate for the Ukrainian standard</abstract>

Department of Information Technologies Security Faculty of Computer Engineering and Control Kharkiv National University of Radioelectronics Lenin’s av., 14 Kharkiv UKRAINE

Department of Informatics Faculty of Mathematics and Natural Sciences University of Bergen Postboks 7803, N-5020 Bergen NORWAY

A Method for Security Estimation of the Spn-Based Block Cipher Against Related-Key Attacks

<abstract><title style='display:none'>Abstract</title>Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix multiplication over the packed ciphertexts. Our packing method generalizes Yasuda et al.’s methods (Security Comm. Networks 2015 and ACISP 2015), which are for secure inner product. We also implement our methods and give a comparison with previous packing methods.</abstract>

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

<abstract><title style='display:none'>Abstract</title> McEliece cryptosystem (MECS) is one of the oldest public key cryptosystems, and the oldest PKC that is conjectured to be post-quantum secure. In this paper we survey the current state of the implementation issues and security of MECS, and its variants. In the first part we focus on general decoding problem, structural attacks, and the selection of parameters in general. We summarize the details of MECS based on irreducible binary Goppa codes, and review some of the implementation challenges for this system. Furthermore, we survey various proposals that use alternative codes for MECS, and point out some attacks on modified systems. Finally, we review notable existing implementations on low-resource platforms, and conclude with the topic of side channels in the implementations of MECS</abstract>

Institute of Computer Science and Mathematics Faculty of Electrical Engineering and Information Technology Slovak University of Technology in Bratislava Ilkovicova 3 SK–812-19 Bratislava SLOVAKIA

Institute of Computer Science and Mathematics Faculty of Electrical Engineering and Information Technology Slovak University of Technology in Bratislava Ilkovicova 3 SK-812-19 Bratislava SLOVAKIA

Overview of the Mceliece Cryptosystem and its Security

<abstract><title style='display:none'>ABSTRACT</title> We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a life- time data set.</abstract>

Department of Social Medicine—FMRP University of S˜ao Paulo Ribeir˜ao Preto, SP BRAZIL

Josmar Mazucheli Department of Statistics University of Maring´a Paran´a BRAZIL

Cure fraction models using mixture and non-mixture models

<abstract><title style='display:none'>Abstract</title> The aim of this paper is to study the oscillation of the second order advanced neutral differential equations <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-011-0006-4#0007_graphic1.png"/></disp-formula>. (E)Obtained results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second order equation to the the oscillation of the first order equations. Obtained comparison principles essentially simplify the examination of the studied equations.</abstract>

Oscillation theorems for second order advanced neutral differential equations