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In this paper, we focus on Brauer's height zero conjecture, Robinson's conjecture, and Olsson's conjecture regarding the direct product of finite groups and give relative versions of these conjectures by restricting them to the algebraic concept of the anchor group of an irreducible character. Consider G to be a finite simple group. We prove that the anchor group of the irreducible character of G with degree p is the trivial group, where p is an odd prime. Additionally, we introduce the relative version of the Green correspondence theorem with respect to this group. We then apply the relative versions of these conjectures to suitable examples of simple groups. Classical and standard theories on the direct product of finite groups, block theory, and character theory are used to achieve these results. [ABSTRACT FROM AUTHOR]

We consider G to be a finite group and p as a prime number. We fix ψ to be an irreducible character of G with its restriction to all p-regular elements of G and ψ 0 to be an irreducible Brauer character. The main aim of this paper is to describe and investigate the relationship between cyclic anchor group of ψ and the defect group of a p-block which contains ψ. Our methods are to study and generalize some facts for the cyclic defect groups of a p-block B to the case of a cyclic anchor group of irreducible characters which belong to B. We establish and prove a criteria for an irreducible character to have a cyclic anchor group. [ABSTRACT FROM AUTHOR]

In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS ( P , π )-code) is also investigated. We extend the concept of I-perfect codes and r-perfect codes to pomset block metric. The relation between I-perfect codes and MDS (P , π) -codes is also considered. When all blocks have the same dimension, we prove the duality theorem for codes and study the weight distribution of MDS pomset block codes when the pomset is a chain. [ABSTRACT FROM AUTHOR]

Congenitally corrected transposition of the great arteries (ccTGA) is a rare congenital anomaly defined by double discordance – atrioventricular and ventricular-arterial. ccTGA frequently has associated lesions, which influence long-term survival. The management of patients with ccTGA regarding the closure of defects and pacing strategies is often very challenging. Moreover, tricuspid valve regurgitation and its impact on the systemic right ventricle requires close monitoring and potentially timely interventions. In this paper, we present and discuss the management challenges raised by a patient with situs inversus totalis, dextrocardia, ccTGA, Ebstein anomaly of the tricuspid valve, atrial septal defect, and complete atrioventricular block. [ABSTRACT FROM AUTHOR]

Let G be a vertex-colored graph. A vertex cut S of G is called a monochromatic vertex cut if the vertices of S are colored with the same color. A graph G is monochromatically vertex-disconnected if any two nonadjacent vertices of G have a monochromatic vertex cut separating them. The monochromatic vertex disconnection number of G , denoted by m v d (G) , is the maximum number of colors that are used to make G monochromatically vertex-disconnected. In this paper, the connection between the graph parameters are studied: m v d (G) , connectivity and block decomposition. We determine the value of m v d (G) for some well-known graphs, and then characterize G when n − 5 ≤ m v d (G) ≤ n and all blocks of G are minimally 2-connected triangle-free graphs. We obtain the maximum size of a graph G with m v d (G) = k for any k. Finally, we study the Erdős-Gallai-type results for m v d (G) , and completely solve them. [ABSTRACT FROM AUTHOR]

As the feature size of integrated circuit decreases, semiconductor devices become more susceptible to Single-Event-Upset (SEU) effect. This paper proposes a radiation hardened latch for Triple-Node-Upset (TNU) tolerance, which can block any triple node upset. Compared with previous radiation hardened TNU Tolerant (TNUT) latches, the proposed Low power-consumption TNUT (LTNUT) latch has the lowest power consumption. When compared with TNU Hardened Latch (TNUHL), TNUT Latch, TNU Completely Tolerant latch (TNUCT), Single-event Multiple-Node Upset Tolerant latch (SMNUT), TNU self-Recoverable Latch (TNURL), Low Cost and TNU-self-Recoverable Latch (LCTNURL) and Quadruple Dual Interlocked Storage Cell (Quadruple-DICE), the proposed LTNUT latch achieves reduction in power consumption by 30.77%, 17.11%, 40%, 20.25%, 20.25%, 27.59% and 64%, respectively. The proposed LTNUT latch achieves reduction in delay by 94.98%, 98.33%, 54.19%, 70.63% and 66.59% when compared with TNUHL, TNUT Latch, SMNUT, TNURL, LCTNURL, respectively, and introduces rise in delay by 3.38% and 5.52%, respectively, when compared with TNUCT and Quadruple-DICE. The proposed LTNUT latch has the lowest power consumption and second smallest delay. The proposed latch is not severely sensitive to temperature and voltage variations. [ABSTRACT FROM AUTHOR]

Let G = (V (G), E(G)) be a simple undirected graph. A block of G is a maximal connected subgraph of G that contains no cut-vertices [11]. The family of vertex sets of blocks of G generates a unique topology. In this paper, we formally define the topology generated by the family of blocks in a graph called the block topological space. Moreover, we characterize and describe some special attributes of the block topological space. Finally, we associate a corresponding graph from a given block topological space by defining the block topological graph. [ABSTRACT FROM AUTHOR]

This paper describes high-frequency nerve block experiments carried out on rat sciatic nerves to measure the speed of recovery of A fibres from block carryover. Block carryover is the process by which nerve excitability remains suppressed temporarily after High Frequency Alternative (HFAC) block is turned off following its application. In this series of experiments 5 rat sciatic nerves were extracted and prepared for ex-vivo stimulation and recording in a specially designed perfusion chamber. For each nerve repeated HFAC block and concurrent stimulation trials were carried out to observe block carryover after signal shutoff. The nerve was allowed to recover fully between each trial. Time to recovery from block was measured by monitoring for when relative nerve activity returned to within 90% of baseline levels measured at the start of each trial. HFAC block carryover duration was found to be dependent on accumulated dose by statistical test for two different HFAC durations. The carryover property of HFAC block on A fibres could enable selective stimulation of autonomic nerve fibres such as C fibres for the duration of carryover. Block carryover is particularly relevant to potential chronic clinical applications of block as it reduces power requirements for stimulation to provide the blocking effect. This work characterizes this process toward the creation of a model describing its behavior. [ABSTRACT FROM AUTHOR]

Flexible surface treatment for exterior pavement applications and the particular requirement to be specific pedestrian walkway design and parking areas are the fundamental feature of paver block identification. The use of conventional materials such as cement, aggregate, and sand is no longer such a priority. Under those circumstances, the production of research-based pavers block has been done to ensure the sustainability and usability of new building materials is expanded. Henceforth, this research is conducted to study and investigate the potential of using waste materials as a partial substitute for aggregate in producing concrete paving block (CPB). In essence, the application of waste materials in concrete paver blocks is highly potential. The innovations in recycling technologies expanded the usage of waste materials to produce paver block products. On the whole, in the manufacturing of concrete, the paper improves and enhances the usability of waste materials. The application of various waste materials such as plastic, steel slag, and crumb rubber is excellent. Compressive strength of paver blocks with different rates of waste steel aggregates and utilizing elastic cushions shows paver blocks give up to 50% more strength quality than customary paver blocks. In terms of the use of industrial waste materials, as a substitute material by reducing the percentage amount of the weight of the cement with the composition ratio varies based on the comparative volume category of the paving block aggregate such as 0%, 5%, 10%, 15%, 20%, and 25% are more applicable. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

Smartphone sensors are widely used in the development of fitness, running, workout, or health applications (apps). However, smartphone sensors may increase the risk of privacy leakage when they bring convenience to users. Traditional access control mechanisms, such as Android Permission, cannot prevent authorized malicious apps from abusing sensor resources. In this paper, a novel behavior-based sensor access control scheme is presented. This scheme can further regulate the behavior of an app after it is authorized, so that it can only access sensor resources with secure behavior patterns (SBPs), and sensor-based privacy leakage may thereby be blocked. On the basis of user interface (UI) operation tracking and tagging, this scheme implements the dynamic perception of app sensor access behaviors. With a temporal logic known as temporal logic of causal knowledge (TLCK), we developed a method to construct the secure sensor access behavior pattern. Every sensor may be given a SBP. By comparing the dynamic sensor access behavior of an app with SBP, we can determine if the sensor access is secure. Moreover, by supervising the call stack of the app's sensor access application programming interface (API), we may timely block a sensor access when it is not secure. In this report, we also describe the implementation of a prototype defense system to analyze the effectiveness and efficiency of the scheme. The experimental results show that this scheme can effectively block the abnormal sensor access of an app with a performance overhead of about 10%. [ABSTRACT FROM AUTHOR]

This paper addresses the two-dimensional strip-packing (2DSP) problem of placing a set of rectangular pieces onto a fixed-width rectangular sheet to minimize the total length used. We propose a Block-Based Heuristic Search Algorithm (BBHSA) to solve 2DSP problems with guillotine cut constraints. Initially, it converts the 2DSP problem into a series of 2D rectangular packing problems (2DRP), where the size of the sheet is fixed. In the BBHSA, rectangular pieces are aggregated into blocks, which are partial solutions without residual space. These blocks provide the ingredients for a good layout and are basic components in a tree-based constructive search process. Two basic operations, called placing & splitting and approximate binary search are used in the search process. Furthermore, several block-based placement rules are explored to speed up the search process and improve solution quality. To verify the performance of our proposed algorithm, we conducted extensive experiments using the zero-waste benchmark and non-zero-waste benchmark instances. The results show that BBHSA demonstrates computational effectiveness, particularly in zero-waste cases, achieving optimal solutions for almost all zero-waste benchmark instances reported in the existing literature. [ABSTRACT FROM AUTHOR]

Abstract The lesser occipital nerve (LON) has one of the most variations among occipital nerves. We aimed to investigate morphological and morphometric features of LON. A total of 24 cadavers, 14 males (58%) and 10 females (42%), were dissected bilaterally. LON was classified into 3 types. The number of branches and the perpendicular distances of the point where LON emerged from the posterior border of sternocleidomastoid muscle to vertical and transverse lines passing through external occipital protuberance were determined. The shortest distance between LON and great auricular nerve (GAN), and linear distance of LON to its branching point were measured. The most common variant was Type 1 (30 sides, 62.5%), followed by Type 2 (12 sides, 25%) and Type 3 (6 sides, 12.5%), respectively. In males, Type 1 (22 sides, 78.6%) was the most common, while Type 1 (8 sides, 40%) and Type 2 (8 sides, 40%) were equally common and the most common in females. On 48 sides, 2–9 branches of LON were observed. The perpendicular distance of said point to vertical and transverse lines was meanly 63.69 ± 11.28 mm and 78.83 ± 17.21 mm, respectively. The shortest distance between LON and GAN was meanly 16.62 ± 10.59 mm. The linear distance of LON to its branching point was meanly 31.24 ± 15.95 mm. The findings reported in this paper may help clinicians in estimating the location of the nerve and/or its branches for block or decompression surgery as well as preservation of LON during related procedures.

Three dimensional packing is a major problem occurring in the transportation sector. It is also a challenging problem to overcome the limitations of existing businesses. This research studies the problem for packing items of Thailand Post (local branches) which provide delivery service to customers and arrange to pack items by staff for delivery to the distribution center. Moreover, the staff want to arrange and pack items into limited roll pallets which must be delivered within the specified period. In this paper, we analyze the problem under the limitations of different types of items and the number of roll pallets and developed an algorithm for sorting and packing items to minimize the amount of items left at the branch when limited roll pallets are available. Moreover, this algorithm can reduce the number of items left at the branch and serve as a guideline for staff. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic 2, let G be a finite group and let B be the principal 2-block of kG with a dihedral or a generalised quaternion defect group P. Let also T (B) denote the group of splendid Morita auto-equivalences of B. We show that T (B) ≅OutP (A) × Out(P,F), where Out(P,F) is the group of outer automorphisms of P which stabilize the fusion system F of G on P and OutP (A) is the group of algebra automorphisms of a source algebra A of B fixing P modulo inner automorphisms induced by (AP)×. [ABSTRACT FROM AUTHOR]

The basic technical element that is a direct response to the opponent's attack is the block. Blocking is related to setting the starting position of the player and choosing the most effective way to move. The aim of this study was to evaluate the time of movement in the block depending on the difficulty of the task determined by a response to light signals. The study included 14 players (17.36 ± 1.18 years). Eight discs of the FITLIGHT TrainerTM device placed at different heights near the center of the volleyball court were used for the measurements. The player's task was to move as quickly as possible in a block after recognizing a light signal to take a specific action. Three types of tasks with different levels of difficulty were defined: reaction to the light signal on the player's side (S1), reaction to the light signal of the upper or lower discs placed vertically over the net (S2), and reaction to the color of the light signal of the upper or lower discs placed vertically over the net (S3). The following time measurements were analyzed: indirect time (TI), time of movement to the jumping point (TJP), and total time (TT) on the right and left sides. In all measurements (TI, TJP, TT), the differences in the times obtained in tasks S1 and S2 and tasks S1 and S3 were statistically significant (p ≤ 0.001) for both the right and left sides. The comparison of the task performance times for S2 and S3 showed a difference only in the TJP measurement for the left side. An analysis of the results indicates a significant role of signal recognition and decision-making process in the player's movement during blocking. The FITLIGHT TrainerTM device can be a useful tool for this purpose in coaching. [ABSTRACT FROM AUTHOR]

Let $ G $ be a vertex-colored graph. A vertex cut $ S $ of $ G $ is called a monochromatic vertex cut if the vertices of $ S $ are colored with the same color. A graph $ G $ is monochromatically vertex-disconnected if any two nonadjacent vertices of $ G $ have a monochromatic vertex cut separating them. The monochromatic vertex disconnection number of $ G $, denoted by $ mvd(G) $, is the maximum number of colors that are used to make $ G $ monochromatically vertex-disconnected. In this paper, the connection between the graph parameters are studied: $ mvd(G) $, connectivity and block decomposition. We determine the value of $ mvd(G) $ for some well-known graphs, and then characterize $ G $ when $ n-5\leq mvd(G)\leq n $ and all blocks of $ G $ are minimally 2-connected triangle-free graphs. We obtain the maximum size of a graph $ G $ with $ mvd(G) = k $ for any $ k $. Finally, we study the Erdős-Gallai-type results for $ mvd(G) $, and completely solve them.

In this paper, we focus on Brauer’s height zero conjecture, Robinson’s conjecture, and Olsson’s conjecture regarding the direct product of finite groups and give relative versions of these conjectures by restricting them to the algebraic concept of the anchor group of an irreducible character. Consider G to be a finite simple group. We prove that the anchor group of the irreducible character of G with degree p is the trivial group, where p is an odd prime. Additionally, we introduce the relative version of the Green correspondence theorem with respect to this group. We then apply the relative versions of these conjectures to suitable examples of simple groups. Classical and standard theories on the direct product of finite groups, block theory, and character theory are used to achieve these results.

The short circuit test of distributed power flow controller (DPFC) is still a blank in the world. In order to test the effectiveness and adaptability of DPFC in case of line failure, it is necessary to carry out short circuit tests in DPFC projects. Based on the Hu Zhou DPFC Project, this paper proposes the control and protect strategy of DPFC which is coordinated with the protect strategy of AC line, designs single phase short circuit grounding test scheme of the AC line where DPFC is located. In the application, the action logic of DPFC under single-phase grounding fault is verified, the single phase short circuit test of DPFC were completed for the first time, and the transient voltage and current were obtained. It provides technical support for the popularization and application of DPFC project.

We consider G to be a finite group and p as a prime number. We fix ψ to be an irreducible character of G with its restriction to all p-regular elements of G and ψ0 to be an irreducible Brauer character. The main aim of this paper is to describe and investigate the relationship between cyclic anchor group of ψ and the defect group of a p-block which contains ψ. Our methods are to study and generalize some facts for the cyclic defect groups of a p-block B to the case of a cyclic anchor group of irreducible characters which belong to B. We establish and prove a criteria for an irreducible character to have a cyclic anchor group.

We derive an asymptotic formula for the number of labeled connected series-parallel -cyclic graphs of a large order with a fixed number . With a uniform probability distribution, we find the probability that a random labeled connected -vertex -cyclic graph with a fixed as is a series-parallel graph. In addition, we determine the probability that, with a uniform probability distribution, a random labeled connected series-parallel -vertex -cyclic graph with a fixed as is a cactus. [ABSTRACT FROM AUTHOR]

Due to the availability of several social media platforms and their use in sending text messages, it is necessary to provide an easy and safe way to protect messages from being hacked especially in the presence of intruders and data thieves, and taking into consideration that most of messages are confidential and personal, it is necessary to provide an easy and safe way to protect messages from being hacked. In this research paper, a simple and easy method of message cryptography will be proposed. The method divides a message into blocks with fixed sizes. The block size ranges from 2 to 60. The method uses a secret color image to generate an array with a size equal to the number of resulted blocks. The array will then be used as a private key. Each element of the private key will be used to calculate the number of rotation digits for the associated block in order to apply block rotation left operation. The proposed method will be examined using the parameters: Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Correlation Coefficient (CC), and throughput. The proposed method will be compared with other standard methods of message cryptography, such as Data Encryption Standard (DES), Triple-DES (3DES), Advanced Encryption Standard (AES), and Blow Fish (BF). Experimental results show that the proposed method is enough secured based on using secret image, block size, and calculated Rotation Left Digits (RLD) for each block.

Three dimensional packing is a major problem occurring in the transportation sector. It is also a challenging problem to overcome the limitations of existing businesses. This research studies the problem for packing items of Thailand Post (local branches) which provide delivery service to customers and arrange to pack items by staff for delivery to the distribution center. Moreover, the staff want to arrange and pack items into limited roll pallets which must be delivered within the specified period. In this paper, we analyze the problem under the limitations of different types of items and the number of roll pallets and developed an algorithm for sorting and packing items to minimize the amount of items left at the branch when limited roll pallets are available. Moreover, this algorithm can reduce the number of items left at the branch and serve as a guideline for staff.

This paper describes high-frequency nerve block experiments carried out on rat sciatic nerves to measure the speed of recovery of A fibres from block carryover. Block carryover is the process by which nerve excitability remains suppressed temporarily after High Frequency Alternative (HFAC) block is turned off following its application. In this series of experiments 5 rat sciatic nerves were extracted and prepared for ex-vivo stimulation and recording in a specially designed perfusion chamber. For each nerve repeated HFAC block and concurrent stimulation trials were carried out to observe block carryover after signal shutoff. The nerve was allowed to recover fully between each trial. Time to recovery from block was measured by monitoring for when relative nerve activity returned to within 90% of baseline levels measured at the start of each trial. HFAC block carryover duration was found to be dependent on accumulated dose by statistical test for two different HFAC durations. The carryover property of HFAC block on A fibres could enable selective stimulation of autonomic nerve fibres such as C fibres for the duration of carryover. Block carryover is particularly relevant to potential chronic clinical applications of block as it reduces power requirements for stimulation to provide the blocking effect. This work characterizes this process toward the creation of a model describing its behavior.