Fundamental Investigations on the Isomorphism of Commutative Group Algebras in Bulgaria

The isomorphism problem of arbitrary algebraic structures plays always a central role in the study of a given algebraic object. In this paper we give the first investigations and also some basic results on the isomorphism problem of commutative group algebras in Bulgaria.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given.

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Design, fabrication, and evaluation of on-chip micro-supercapacitors

Due to the increasing demand for high power and reliable miniaturized energy storage devices, the development of micro-supercapacitors or electrochemical micro-capacitors have attracted much attention in recent years. This dissertation investigates several strategies to develop on-chip micro-supercapacitors with high power and energy density. Micro-supercapacitors based on interdigitated carbon micro-electrode arrays are fabricated through carbon microelectromechanical systems (C-MEMS) technique which is based on carbonization of patterned photoresist. To improve the capacitive behavior, electrochemical activation is performed on carbon micro-electrode arrays. The developed micro-supercapacitors show specific capacitances as high as 75 mFcm-2 at a scan rate of 5 mVs -1 after electrochemical activation for 30 minutes. The capacitance loss is less than 13% after 1000 cyclic voltammetry (CV) cycles. These results indicate that electrochemically activated C-MEMS micro-electrode arrays are promising candidates for on-chip electrochemical micro-capacitor applications. The energy density of micro-supercapacitors was further improved by conformal coating of polypyrrole (PPy) on C-MEMS structures. In these types of micro-devices the three dimensional (3D) carbon microstructures serve as current collectors for high energy density PPy electrodes. The electrochemical characterizations of these micro-supercapacitors show that they can deliver a specific capacitance of about 162.07 mFcm-2 and a specific power of 1.62mWcm -2 at a 20 mVs-1 scan rate. Addressing the need for high power micro-supercapacitors, the application of graphene as electrode materials for micro-supercapacitor was also investigated. The present study suggests a novel method to fabricate graphene-based micro-supercapacitors with thin film or in-plane interdigital electrodes. The fabricated micro-supercapacitors show exceptional frequency response and power handling performance and could effectively charge and discharge at rates as high as 50 Vs-1. CV measurements show that the specific capacitance of the micro-supercapacitor based on reduced graphene oxide and carbon nanotube composites is 6.1 mFcm -2 at scan rate of 0.01Vs-1. At a very high scan rate of 50 Vs-1, a specific capacitance of 2.8 mFcm-2 (stack capacitance of 3.1 Fcm-3) is recorded. This unprecedented performance can potentially broaden the future applications of micro-supercapacitors.

Integrity-based kernel malware detection

Kernel-level malware is one of the most dangerous threats to the security of users on the Internet, so there is an urgent need for its detection. The most popular detection approach is misuse-based detection. However, it cannot catch up with today's advanced malware that increasingly apply polymorphism and obfuscation. In this thesis, we present our integrity-based detection for kernel-level malware, which does not rely on the specific features of malware. ^ We have developed an integrity analysis system that can derive and monitor integrity properties for commodity operating systems kernels. In our system, we focus on two classes of integrity properties: data invariants and integrity of Kernel Queue (KQ) requests. ^ We adopt static analysis for data invariant detection and overcome several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We identify data invariants that are critical to system runtime integrity from Linux kernel 2.4.32 and Windows Research Kernel (WRK) with very low false positive rate and very low false negative rate. We then develop an Invariant Monitor to guard these data invariants against real-world malware. In our experiment, we are able to use Invariant Monitor to detect ten real-world Linux rootkits and nine real-world Windows malware and one synthetic Windows malware. ^ We leverage static and dynamic analysis of kernel and device drivers to learn the legitimate KQ requests. Based on the learned KQ requests, we build KQguard to protect KQs. At runtime, KQguard rejects all the unknown KQ requests that cannot be validated. We apply KQguard on WRK and Linux kernel, and extensive experimental evaluation shows that KQguard is efficient (up to 5.6% overhead) and effective (capable of achieving zero false positives against representative benign workloads after appropriate training and very low false negatives against 125 real-world malware and nine synthetic attacks). ^ In our system, Invariant Monitor and KQguard cooperate together to protect data invariants and KQs in the target kernel. By monitoring these integrity properties, we can detect malware by its violation of these integrity properties during execution.^

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Éléments réguliers du groupe H₄

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Sur les solutions invariantes et conditionnellement invariantes des équations de la magnétohydrodynamique

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Influence of alkyl chain length on sulfated zirconia catalysed batch and continuous esterification of carboxylic acids by light alcohols

The impact of alkyl chain length on the esterification of C2–C16 organic acids with C1–C4 alcohols has been systematically investigated over bulk and SBA-15 supported sulfated zirconias (SZs). Rates of catalytic esterification for methanol with acetic acid are directly proportional to the sulfur content for both SZ and SZ/SBA-15, with the high dispersion of SZ achievable in conformal coatings over mesoporous SBA-15 confering significant rate-enhancements. Esterification over the most active 0.24 mmol gcat−1 bulk SZ and 0.29 mmol gcat−1 SZ/SBA-15 materials was inversely proportional to the alkyl chain length of alcohol and acid reactants; being most sensitive to changes from methanol to ethanol and acetic to hexanoic acids respectively. Kinetic analyses reveal that these alkyl chain dependencies are in excellent accord with the Taft relationship for polar and steric effects in aliphatic systems and the enthalpy of alcohol adsorption, implicating a Langmuir–Hinshelwood mechanism. The first continuous production of methyl propionate over a SZ fixed-bed is also demonstrated.

Vacuum spacetimes with constant Weyl eigenvalues

Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant A) with constant non-zero Weyl eigenvalues are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2A/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant.

Nanostructured Metal Oxide Coatings for Electrochemical Energy Conversion and Storage Electrodes

The realization of an energy future based on safe, clean, sustainable, and economically viable technologies is one of the grand challenges facing modern society. Electrochemical energy technologies underpin the potential success of this effort to divert energy sources away from fossil fuels, whether one considers alternative energy conversion strategies through photoelectrochemical (PEC) production of chemical fuels or fuel cells run with sustainable hydrogen, or energy storage strategies, such as in batteries and supercapacitors. This dissertation builds on recent advances in nanomaterials design, synthesis, and characterization to develop novel electrodes that can electrochemically convert and store energy.

Chapter 2 of this dissertation focuses on refining the properties of TiO2-based PEC water-splitting photoanodes used for the direct electrochemical conversion of solar energy into hydrogen fuel. The approach utilized atomic layer deposition (ALD); a growth process uniquely suited for the conformal and uniform deposition of thin films with angstrom-level thickness precision. ALD’s thickness control enabled a better understanding of how the effects of nitrogen doping via NH3 annealing treatments, used to reduce TiO2’s bandgap, can have a strong dependence on TiO2’s thickness and crystalline quality. In addition, it was found that some of the negative effects on the PEC performance typically associated with N-doped TiO2 could be mitigated if the NH3-annealing was directly preceded by an air-annealing step, especially for ultrathin (i.e., < 10 nm) TiO2 films. ALD was also used to conformally coat an ultraporous conductive fluorine-doped tin oxide nanoparticle (nanoFTO) scaffold with an ultrathin layer of TiO2. The integration of these ultrathin films and the oxide nanoparticles resulted in a heteronanostructure design with excellent PEC water oxidation photocurrents (0.7 mA/cm2 at 0 V vs. Ag/AgCl) and charge transfer efficiency.

In Chapter 3, two innovative nanoarchitectures were engineered in order to enhance the pseudocapacitive energy storage of next generation supercapacitor electrodes. The morphology and quantity of MnO2 electrodeposits was controlled by adjusting the density of graphene foliates on a novel graphenated carbon nanotube (g-CNT) scaffold. This control enabled the nanocomposite supercapacitor electrode to reach a capacitance of 640 F/g, under MnO2 specific mass loading conditions (2.3 mg/cm2) that are higher than previously reported. In the second engineered nanoarchitecture, the electrochemical energy storage properties of a transparent electrode based on a network of solution-processed Cu/Ni cores/shell nanowires (NWs) were activated by electrochemically converting the Ni metal shell into Ni(OH)2. Furthermore, an adjustment of the molar percentage of Ni plated onto the Cu NWs was found to result in a tradeoff between capacitance, transmittance, and stability of the resulting nickel hydroxide-based electrode. The nominal area capacitance and power performance results obtained for this Cu/Ni(OH)2 transparent electrode demonstrates that it has significant potential as a hybrid supercapacitor electrode for integration into cutting edge flexible and transparent electronic devices.