Sharif Digital Repository

Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights.
The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to... 

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR. To evaluate the resistance of an ARX cipher against differential and impossible-differential cryptanalysis, the recent automated methods employ constraint satisfaction solvers to search for optimal characteristics or impossible differentials. The main difficulty in formulating this search is finding the differential models of the non-linear operations. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this... 

In this article, the homotopy analysis method has been applied to solve nonlinear differential equations of fractional order. The validity of this method has successfully been accomplished by applying it to find the solution of two nonlinear fractional equations. The results obtained by homotopy analysis method have been compared with those exact solutions. The results show that the solution of homotopy analysis method is good agreement with the exact solution. Crown  

KLEIN is a family of lightweight block ciphers which was proposed at RFIDSec 2011 by Gong et. al. It has three versions with 64, 80 or 96-bit key size, all with a 64-bit state size. It uses 16 identical 4-bit S-boxes combined with two AES's MixColumn transformations for each round. This approach allows compact implementations of KLEIN in both low-end software and hardware. Such an unconventional combination attracts the attention of cryptanalysts, and several security analyses have been published. The most successful one was presented at FSE 2014 which was a truncated differential attack. They could attack up to 12, 13 and 14 rounds out of total number of 12, 16 and 20 rounds for... 

We consider the nonlinear Euler differential equation t2 x″ + g (x) = 0. Here g (x) satisfies x g (x) > 0 for x ≠ 0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t2 x″ + a (t) g (x) = 0. © 2006 Elsevier Inc. All rights reserved  

This paper studies undamped oscillations of fractional-order Duffing system. Stability theorems for fractional order systems are used to determine the characteristic polynomial of the system in order to find the parametric ranges for undamped oscillations in this system. We also derive relations for estimating the frequency and the amplitude of the oscillations in this system using a describing function method. Finally numerical simulation results are provided to justify the analysis  

In this study vibration amplitude, frequency and damping of a microbeam is controlled using a RLC block containing a capacitor, resistor and inductor in series with the microbeam. Applying this method all of the considerable characteristics of the oscillatory system can be determined and controlled with no change in the geometrical and physical characteristics of the microbeam. Euler-Bernoulli assumptions are made for the microbeam and the electrical current through the microbeam is computed by considering the microbeam deflection and its voltage. Considering the RLC block, the voltage difference between the microbeam and the substrate is calculated. Two coupled nonlinear partial... 

This paper analyzes the Piccolo family of lightweight block ciphers against the impossible differential cryptanalysis. A combination of some ploys such as decreasing the S-box computations, finding an appropriate propagation of differentials, utilizing hash tables and using the linearity of the key-schedule as well as disregarding subkeys of two rounds lead to 12-round and 13-round impossible differential attack on Piccolo-80 and 15-round attack on Piccolo-128. The time and data complexity of the attack against Piccolo-80 is 255.18 and 236.34 for 12-round and 269.7 and 243.25 for 13-round, respectively. Moreover, the time and data complexity for 15 rounds cryptanalysis of Piccolo-128 are... 

TEA and XTEA are two lightweight Feistel block ciphers, each of which has a block size of 64 bits and a key size of 128 bits. These two ciphers have ARX structure, i.e. their round functions consist of modular addition, shift and XOR to be exact. Since each operation of TEA and XTEA can be done in a bitwise fashion, we are able to use early abort technique in the impossible differential attack that helps us to remove inappropriate pairs as soon as possible, hence decreasing time complexity. In this paper we present two new 15-round impossible differential characteristics, resulting in the first known impossible differential cryptanalysis mounted on 19 rounds of TEA and 25 rounds of XTEA  

Various natural and modified polysaccharides (i.e. arabic gum, tragacanth gum, xanthan gum, sodium alginate, chitosan, sodium carboxymethyl cellulose, hydroxyethyl cellulose, methyl cellulose) were modified using ceric-initiated graft polymerization of acrylonitrile under inert atmosphere. Grafting was confirmed using spectral (FT-IR) proofs. The grafting parameters were determined by conventional methods. Thermal characteristics of the homopolymer-free copolymers were studied using differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) under nitrogen atmosphere. The major thermal transitions as well as the activation energy of the major decomposition stages were... 

In this study, the authors study a fibre-optic local area network deploying optical code division multiple access technique with differential M-ary pulse position modulation (DPPM). The authors present the performance analysis of DPPM signalling using a double optical hardlimiter receiver structure considering the impairment caused by interference of other users. The analysis assumes a set of bit asynchronous transmitters employing generalised optical orthogonal codes for their DPPM signalling (GOOC-DPPM). Using mathematical analysis and simulations, the authors have demonstrated that GOOCDPPM improves both frame error probability and the maximum achievable network throughput compared with... 

Recent research works demonstrated that the interaction between the loads and the carrying structure's boundary which is related to the inertia of the load is an influential factor on the dynamic response of the structure. Although effects of the inertia in moving loads were considered in many works, very few papers can be found on the inertial effects of the stationary loads on structures. In this paper, an elastodynamic formulation was employed to investigate the dynamic response of a homogeneous isotropic elastic half-space under an inertial strip foundation subjected to a time-harmonic force. Fourier integral transformation was used to solve the system of Poisson-type partial... 

We study the concept and the calculus of Non-convex self-dual (Nc-SD) Lagrangians and their derived vector fields which are associated to many partial differential equations and evolution systems. They indeed provide new representations and formulations for the superposition of convex functions and symmetric operators. They yield new variational resolutions for large class of Hamiltonian partial differential equations with variety of linear and nonlinear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to... 

One subcategory of project scheduling is the resource constrained project scheduling problem (RCPSP). The present study proposes a differential evolution algorithm for solving the RCPSP making a small change in the method to comply with the model. The RCPSP is intended to program a group of activities of minimal duration while considering precedence and resource constraints. The present study introduces a differential evolution algorithm and local search was added to improve the performance of the algorithm. The problems were then solved to evaluate the performance of the algorithm and the results are compared with genetic algorithm. Computational results confirm that the differential... 

Impossible differential attack is a well-known mean to examine robustness of block ciphers. Using impossible differential cryptanalysis, we analyze security of a family of lightweight block ciphers, named Midori, that are designed considering low energy consumption. Midori state size can be either 64 bits for Midori64 or 128 bits for Midori128; however, both versions have key size equal to 128 bits.In this paper, we mainly study security of Midori64. To this end, we use various techniques such as early-abort, memory reallocation, miss-in-the-middle and turning to account the inadequate key schedule algorithm of Midori64. We first show two new 7-round impossible differential characteristics... 

We introduce a universal and systematic way of defining a generalized B-spline based on a linear shift-invariant (LSI) operator L (a.k.a. Fourier multiplier). The generic form of the B-spline is βL=LdL−1δ where L−1δ is the Green's function of L and where Ld is the discretized version of the operator that has the smallest-possible null space. The cornerstone of our approach is a main construction of Ld in the form of an infinite product that is motivated by Weierstrass’ factorization of entire functions. We show that the resulting Fourier-domain expression is compatible with the construction of all known B-splines. In the special case where L is the derivative operator (linked with... 

Optimal queuing system design includes deciding about some variables such as location, capacity, price, and delivery time. In order to develop an optimized system, it is essential to solve the optimization problem for all the decision variables simultaneously. In this paper, a make-to-order system is considered. In this system, some facilities are developed in different points. According to the make-to-order system definition, these facilities keep no inventory from final product. Orders are received from customers and the requested products are assembled. Due to existence of some differences among customers, they are divided into two distinct categories including express and regular... 

In this paper, we describe an impossible differential property for 2.5 rounds of Safer++. It allows an impossible differential attack on 4 rounds of Safer++. The proposed attack requires 2 23 chosen plaintexts and 2 75 bytes of memory and performs 2 84 4-round Safer++ encryptions. The method developed to attack Safer++ can be applied to other block ciphers in Safer family. 1  

Using two techniques of thermogravimetry and differential scanning calorimetry under O2 gas atmosphere from 25 to 600°C, the thermal behavior of laboratory-produced compound lead(IV) oxide α-PbO2 was investigated. The identity of products at different stages were confirmed by XRD technique. Both techniques produced similar results supporting the same decomposition stages for the compound. Three distinct energy changes were observed, namely, two endothermic and one exothermic in DSC. The amount of ΔH for each peak is also reported. © 2008 Springer Science+Business Media, LLC