Number Of Certain Classes Research Articles

A few projective classes of (non-Hausdorff) topological spaces

A class of topological spaces is projective (resp., ω-projective) if and only if projective systems of spaces (resp., with a countable cofinal subset of indices) in the class are still in the class. A certain number of classes of Hausdorff spaces are known to be, or not to be, (ω-) projective. We examine classes of spaces that are not necessarily Hausdorff. Sober and compact sober spaces form projective classes, but most classes of locally compact spaces are not even ω-projective. Guided by the fact that the stably compact spaces are exactly the locally compact, strongly sober spaces, and that the strongly sober spaces are exactly the sober, coherent, compact, weakly Hausdorff (in the sense of Keimel and Lawson) spaces, we examine which classes defined by combinations of those properties are projective. Notably, we find that coherent sober spaces, compact coherent sober spaces, as well as (locally) strongly sober spaces, form projective classes.

Average distance colouring of graphs

Abstract For a graph G with n vertices, average distance µ(G) is the ratio of sum of the lengths of the shortest paths between all pairs of vertices to the number of edges in a complete graph on n vertices. In this paper, we introduce average distance colouring and find the average distance colouring number of certain classes of graphs.

THE GEODETIC FAULT TOLERANT DOMINATION NUMBER OF A GRAPH

For a connected graph G = (V,E), a set F ⊆ V of vertices in G is called dominating set if every vertex not in F has at least one neighbor in F. A dominating set F ⊆ V is called fault tolerant dominating set if F − {v} is dominating set for every v ∈ F. A fault tolerant dominating set is said to be geodetic fault tolerant dominating set if I[F] = V . The minimum cardinality of a geodetic fault tolerant dominating set is called geodetic fault tolerant domination number and is denoted by γgft(G). The minimum geodetic fault tolerant dominating set is denoted by γgft-set. The geodetic fault tolerant domination number of certain classes of graphs are determined. Some general properties satisfied by this concept are studied. It is shown that for every positive integer 2 < a ≤ b there is a connected graph G such that γ(G) = a, γg(G) = b and γgft(G) = a + b − 2, where γ(G) and γg(G) are the domination number and geodetic domination number of G respectively.

The Upper Connected Outer Connected Monophonic Number of a Graph

For a connected graph of order at least two, a connected outer connected monophonic set of is called a minimal connected outer connected monophonic set if no proper subset of is a connected outer connected monophonic set of . The upper connected outer connected monophonic number of is the maximum cardinality of a minimal connected outer connected monophonic set of . We determine bounds for it and find the upper connected outer connected monophonic number of certain classes of graphs. It is shown that for any two integers with , there is a connected graph of order with and . Also, for any three integers and with , there is a connected graph with and and a minimal connected outer connected monophonic set of cardinality , where is the connected outer connected monophonic number of a graph.

DLPR: Deep Learning-Based Enhanced Pattern Recognition Frame-Work for Improved Myoelectric Prosthesis Control

In EMG based pattern recognition (EMG-PR), deep learning-based techniques have become more prominent for their self-regulating capability to extract discriminant features from large data-sets. Moreover, the performance of traditional machine learning-based methods show limitation to categorize over a certain number of classes and degrades over a period of time. In this paper, an accurate, robust, and fast convolutional neural network-based framework for EMG pattern identification is presented. To assess the performance of the proposed system, five publicly available and benchmark data-sets of upper limb activities were used. This data-set contains 49 to 52 upper limb motions (NinaPro DB1, NinaPro DB2, and NinaPro DB3), Data with force variation, and data with arm position variation for intact and amputated subjects. The classification accuracies of 92.18% (53 classes), 91.56% (49 classes), 84.98% (49 classes of amputees), 95.67% (6 classes with force variation), and 99.12% (8 classes with arm position variation) have been observed during the testing. The performance of the proposed system is compared with the state of art techniques in the literature. The findings demonstrate that classification accuracy and time complexity have been improved significantly. For signal pre-processing and deep learning techniques, Keras which is a high-level API for TensorFlow is utilised to build profound learning models. The proposed method has been tested on the Intel Core i7 3.5GHz, 7th Gen CPU with 8GB DDR4 RAM.

Numerical radius and Berezin number inequality

We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular, we show that for any scalar-valued non-constant inner function θ, the numerical radius and the Crawford number of a Toeplitz operator Tθ on a Hardy space is 1 and 0, respectively. It is also shown that numerical radius is multiplicative for a class of isometries and sub-multiplicative for a class of commutants of a shift. We have illustrated these results with some concrete examples. Finally, some Hardy-type inequalities for Berezin number of certain class of operators are established with the help of the classical Hardy's inequality.

On the correlation between a sub-level qualifier refining the danger level with observations and models relating to the contributing factors of avalanche danger

Abstract. Forecasting avalanche danger at a regional scale is a largely data-driven yet also experience-based decision-making process by human experts. In the case of public avalanche forecasts, this assessment process terminates in an expert judgment concerning summarizing avalanche conditions by using one of five danger levels. This strong simplification of the continuous, multi-dimensional nature of avalanche hazard allows for efficient communication but inevitably leads to a loss of information when summarizing the severity of avalanche hazard. Intending to overcome the discrepancy between determining the final target output in higher resolution while maintaining the well-established standard of assessing and communicating avalanche hazard using the avalanche danger scale, avalanche forecasters at the national avalanche warning service in Switzerland used an approach that combines absolute and relative judgments. First, forecasters make an absolute judgment using the five-level danger scale. In a second step, a relative judgment is made by specifying a sub-level describing the avalanche conditions relative to the chosen danger level. This approach takes into account the human ability to reliably estimate only a certain number of classes. Here, we analyze these (yet unpublished) sub-levels, comparing them with data representing the three contributing factors of avalanche hazard: snowpack stability, the frequency distribution of snowpack stability, and avalanche size. We analyze both data used in operational avalanche forecasting and data independent of the forecast, going back 5 years. Using a sequential analysis, we first establish which data are suitable and in which part of the danger scale they belong by comparing their distributions at consecutive danger levels. In a second step, integrating these findings, we compare the frequency of locations with poor snowpack stability and the number and size of avalanches with the forecast sub-level. Overall, we find good agreement: a higher sub-level is generally related to more locations with poor snowpack stability and more avalanches of larger size. These results suggest that on average avalanche forecasters can make avalanche danger assessments with higher resolution than the five-level danger scale. Our findings are specific to the current forecast set-up in Switzerland. However, we believe that avalanche warning services making a hazard assessment using a similar temporal and spatial scale as currently used in Switzerland should also be able to refine their assessments if (1) relevant data are sufficiently available in time and space and (2) a similar approach combining absolute and relative judgment is used. The sub-levels show a rank-order correlation with data related to the three contributing factors of avalanche hazard. Hence, they increase the predictive value of the forecast, opening the discussion on how this information could be provided to forecast users.

Forcing edge detour monophonic number of a graph

‎For a connected graph $G=(V,E)$ of order at least two‎, ‎an edge detour monophonic set of $G$ is a set $S$ of vertices such that every edge of $G$ lies on a detour monophonic path joining some pair of vertices in $S$‎. ‎The edge detour monophonic number of $G$ is the minimum cardinality of its edge detour monophonic sets and is denoted by $edm(G)$‎. ‎A subset $T$ of $S$ is a forcing edge detour monophonic subset for $S$ if $S$ is the unique edge detour monophonic set of size $edm(G)$ containing $T$‎. ‎A forcing edge detour monophonic subset for $S$ of minimum cardinality is a minimum forcing edge detour monophonic subset of $S$‎. ‎The forcing edge detour monophonic number $f_{edm}(S)$ in $G$ is the cardinality of a minimum forcing edge detour monophonic subset of $S$‎. ‎The forcing edge detour monophonic number of $G$ is $f_{edm}(G)=min{f_{edm}(S)}$‎, ‎where the minimum is taken over all edge detour monophonic sets $S$ of size $edm(G)$ in $G$‎. ‎We determine bounds for it and find the forcing edge detour monophonic number of certain classes of graphs‎. ‎It is shown that for every pair a‎, ‎b of positive integers with $0leq a<b$ and $bgeq 2$‎, ‎there exists a connected graph $G$ such that $f_{edm}(G)=a$ and $edm(G)=b$‎.

The forcing total monophonic number of a graph

For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum forcing total monophonic subset of S. The forcing total monophonic number ftm(S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is ftm(G) = min{ftm(S)}, where the minimum is taken over all minimum total monophonic sets S in G. We determine bounds for it and find the forcing total monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 ≤ a &lt; b and b ≥ a+4, there exists a connected graph G such that ftm(G) = a and mt(G) = b.

The monophonic global domination number of a graph

A set M ⊆ V is said to be a monophonic global dominating set of G if M is both a monophonic set and a global dominating set of G. The minimum cardinality of a monophonic global dominating set of G is the monophonic global domination number of G and is denoted by γm(G). A monophonic global dominating set of cardinality γm(G) is called a γm-set of G. The monophonic global domination number of certain classes of graphs are determined. It is proved that 2 ≤ γm(G) ≤ γg (G) ≤ n, where γg (G) is a geodetic global domination number of a G. It is shown that for every pair of positive integers a and b with 2 ≤ a ≤ b, there exists a connected graph G such that γm(G) = a and γg (G) = b.

Restrained geodetic domination in graphs

Let [Formula: see text] be a graph with edge set [Formula: see text] and vertex set [Formula: see text]. For a connected graph [Formula: see text], a vertex set [Formula: see text] of [Formula: see text] is said to be a geodetic set if every vertex in [Formula: see text] lies in a shortest path between any pair of vertices in [Formula: see text]. If the geodetic set [Formula: see text] is dominating, then [Formula: see text] is geodetic dominating set. A vertex set [Formula: see text] of [Formula: see text] is said to be a restrained geodetic dominating set if [Formula: see text] is geodetic, dominating and the subgraph induced by [Formula: see text] has no isolated vertex. The minimum cardinality of such set is called restrained geodetic domination (rgd) number. In this paper, rgd number of certain classes of graphs and 2-self-centered graphs was discussed. The restrained geodetic domination is discussed in graph operations such as Cartesian product and join of graphs. Restrained geodetic domination in corona product between a general connected graph and some classes of graphs is also discussed in this paper.

Assessing a multidimensional model of police legitimacy in South Korea with latent class analysis

ABSTRACT There are few validated scales for police legitimacy, and the ambiguous dimensionality of legitimacy raises a serious issue. This study tests a multidimensional scale of legitimacy, drawing upon the police legitimacy model. To identify a certain number of classes with a similar pattern of hypothesized legitimacy among a nationally representative sample of South Korean adults, we employed latent class analysis that legitimacy researchers have yet to consider. The current study found that police legitimacy was constituted with the four sub-dimensions of lawfulness, procedural fairness, police effectiveness, and equitable distribution of police sanctions. South Korean adults within the four multidimensional legitimacy scales were separated into three clusters: the legal procedure-oriented group (41.6%), the equitable sanction-oriented group (20.8%), and the cynic-oriented group (37.6%). The odds of self-reported complying with police requests and cooperating with the police were higher among members in both the legal procedure-oriented and equitable sanction-oriented groups compared to those in the cynic-oriented group. Finally, the four multidimensional legitimacy scales had a direct effect on both self-reported compliance and cooperation and had a mediating effect on the relationship between obligation to obey and both outcome variables. We conclude that police in South Korea should enhance the four multidimensions of legitimacy during each encounter with the public.

The upper restrained Steiner number of a graph

A Steiner set [Formula: see text] of a connected graph [Formula: see text] of order [Formula: see text] is a restrained Steiner set if either [Formula: see text] or the subgraph [Formula: see text] has no isolated vertices. The minimum cardinality of a restrained Steiner set of [Formula: see text] is the restrained Steiner number of [Formula: see text], and is denoted by [Formula: see text]. A restrained Steiner set [Formula: see text] in a connected graph [Formula: see text] is called a minimal restrained Steiner set if no proper subset of [Formula: see text] is a restrained Steiner set of [Formula: see text]. The upper restrained Steiner number [Formula: see text] is the maximum cardinality of a minimal restrained Steiner set of [Formula: see text]. The upper restrained Steiner number of certain classes of graphs are determined. Connected graphs of order [Formula: see text] with upper restrained Steiner number [Formula: see text] or [Formula: see text] are characterized. It is shown that for every pair of integers [Formula: see text] and [Formula: see text], with [Formula: see text], there exists a connected graph [Formula: see text] such that [Formula: see text] and [Formula: see text]. Also, it is shown that for every pair of integers [Formula: see text] and [Formula: see text] with [Formula: see text] there exists a connected graph [Formula: see text] with [Formula: see text] and [Formula: see text], where [Formula: see text] is the upper restrained geodetic number of the graph [Formula: see text].

The Forcing Restrained Steiner Number of a Graph

A restrained Steiner set of a connected graph 𝑮 of order 𝒑≥𝟐 is a set 𝑾⊆𝑽(𝑮)such that 𝑾 is a Steiner set, and if either 𝑾 = 𝑽 or the subgraph𝑮[𝑽−𝑾] inducedby [𝑽−𝑾] has no isolated vertices. The restrained Steiner number 𝒔𝒓(𝑮) of 𝑮 isthe minimum cardinality of its restrained Steiner sets and any restrained Steinerset of cardinality 𝒔𝒓(𝑮) is a minimum restrained Steiner set of 𝑮. For a minimum restrained Steiner set 𝑾of 𝑮, a subset 𝑻⊆𝑾 is called a forcing subset for 𝑾 if 𝑾is the unique minimum restrained Steiner set containing 𝑻. A forcing subset for 𝑾of minimum cardinality is a minimum forcing subset of 𝑾. The forcing restrained Steiner number of 𝑾, denoted by 𝒇𝒓𝒔(𝑾), is the cardinality of a minimum forcingsubset of 𝑾. The forcing restrained Steiner number of 𝑮, denoted by 𝒇𝒓𝒔(𝑮)is𝒇𝒓𝒔(𝑮)=𝒎𝒊𝒏 {𝒇𝒓𝒔(𝑾)}, where the minimum is taken over all minimum restrainedSteiner sets 𝑾 in 𝑮. Some general properties satisfied by the concept forcing restrained Steiner number are studied. The forcing restrained Steiner number of certain classes of graphs is determined. It is shown that for every pair 𝒂,𝒃 ofintegers with 𝟎≤𝒂 &lt; 𝒃and 𝒃≥𝟐, there exists a connected graph 𝑮 such that𝒇𝒓𝒔(𝑮)=𝒂 and 𝒔𝒓(𝑮)=𝒃.

Radio Geometric graceful graphs

A one-one mapping f : V (G) → Z+ satisfying the condition , for every pair of distinct vertices in G is defined as radio geometric mean labeling of G. The maximum number assigned to any vertex of G under the labeling f is called its radio geometric mean number of f denoted rgmn(f). The least value of rgmn(f), taken over all such labelings f of G is defined as its radio geometric mean number and is denoted by rgmn(G). Clearly, rgmn(G) ≥ |V(G)|. Graphs for which rgmn(G) = |V(G)| are defined as radio geometric graceful. In this paper, we find the radio geometric mean number of certain classes of graphs like sunflowers, Helms, gear graphs and show that they are radio geometric graceful.

On the (M, D) number of a graph

For a connected graph G = (V, E), a monophonic set of G is a set M ⊆ V (G) such that every vertex of G is contained in a monophonic path joining some pair of vertices in M. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbour in D. A monophonic dominating set M is both a monophonic and a dominating set. The monophonic, dominating, monophonic domination number m(G), γ(G), γm(G) respectively are the minimum cardinality of the respective sets in G. Monophonic domination number of certain classes of graphs are determined. Connected graph of order p with monophonic domination number p− 1 or p is characterised. It is shown that for every two intigers a, b ≥ 2 with 2 ≤ a ≤ b, there is a connected graph G such that γm(G) = a and γg(G) = b, where γg(G) is the geodetic domination number of a graph.

An integrated design approach for class-based block stacked warehouse

PurposeThis paper aims to develop an approach to design a warehouse that uses class-based storage policy in a way that minimizes both space cost and material handling cost.Design/methodology/approachThe authors argue for and develop an optimization model for joint determination of lane depth, lateral width and product partitions for minimizing the sum of handling and space costs. In doing so, the assumption of perfect sharing is also relaxed. Using computational experiments, the authors characterize the operating conditions based on pick density and cost ratio. The authors further outline an approach to decide the conditions under which it is advantageous to implement multiple classes.FindingsMore classes are preferred when both the pick density and cost ratio are higher and vice versa. Factors such as demand skewness, lane depth and stacking height affect the space-sharing dynamics.Practical implicationsThe paper gives the practical insights on when the conditions under which it is advisable to partition a warehouse into a certain number of classes instead of maintaining and when to maintain as a single-class block. It also gives a method to estimate the space-sharing factor, given a combination of operating parameters.Originality/valueVery few studies have seen class-based storage policy in the context of block stacked warehouse layout. Further, block stacking designs have mostly been approached with the objective of minimizing just the space cost. This study contributes to the literature by developing an integrated model, which has the practical utility.

Комбінаторний інваріант для функції, заданої на колі

The article deals with the case of continuous functions with a finite number of local extrema defined on a one-dimensional compact manifold without boundary. The conditions of topological equivalence of continuous functions on S 1 are investigated. A combinatorial invariant for the function f is constructed and it is determined that for the class of functions in question the complete combinatorial invariants must coincide. One of the problems of topology is the study of conditions for the topological equivalence of functions on manifolds. Determining the number of topologically nonequivalent functions on a circle reduces to combinatorics of permutations. But in nature, there are functions for which at least two local extremes correspond to one critical value. In this case, a combinatorial invariant should be introduced - a set of periodic alternating sequences. However, the number of such periodic alternating sequences is not defined, so it is advisable to construct an invariant that will allow you to specify the number of certain classes of functions on a circle and obtain estimates for the general case. The purpose of the study is to investigate the relationship between continuous functions on a circle and their combinatorial invariants to determine the topological equivalence of functions. An invariant of a function that answers the questions posed is alternating sequences, with the help of which a sequence of values of a function is constructed. In the case when the number of local extremes of the function coincides with the number of critical values, then the invariant is a snake. But not all snakes are possible, because the position of the last maximum of the snake depends on the position of the first minimum of the next snake. The article considers the general case when the number of critical values of a function is not equal to the number of local extremes and the function has m global maxima (minima). The invariant of such a function is the division of the circle into arcs, the value of the function in their local extremum, form elementary snakes. It is proved that a necessary and sufficient condition for the topological equivalence of two functions on a circle is an isomorphism of partitions, which is answered by them. Keywords: partitions, arc, function on a circle, invariant, topological equivalence, local extremum

Edge-to-vertex m-detour monophonic number of a graph

For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour monophonic path joining a pair of edges of S. The edge-to-vertex mdetour monophonic number Dmev(G) of G is the minimum order of its edge-to-vertex m-detour monophonic sets and any edge-to-vertex m-detour monophonic set of order Dmev(G) is an edge-to-vertex mdetour monophonic basis of G. Some general properties satisfied by this parameter are studied. The edge-to-vertex m-detour monophonic number of certain classes of graphs are determined. It is shown that for positive integers r, d and k ≥ 4 with r < d, there exists a connected graph G such that radm(G) = r, diamm(G) = d and Dmev(G) = k

Null function classification using NFR matrix and decision tree

This research work is based on the classification of the functions which are required and which is not required for the efficient development of the software. The motivation of this work is to identify non required functions to reduce development cost and efforts. The classification is the technique which can classify data into certain number of classes. The NFR matrix is the existing technique which can classify the Null functions. To classify the null functions NFR use clustering method which can modify to increase accuracy of classification. In the existing method NFR matrix is used for the null function classification, it use the clustering for the classification. In this work, decision tree will based with the clustering. It take input result of clustering and generate classified result.