Ordinal Operators Research Articles

Influence of condenser bypass port area on maximum thermal load of heat pipe

Experimental works have been conducted to enhance the performance of heat pipes by focusing on the maximum thermal load, which is a very important performance indicator. Ordinal operation on the heat pipe occurs when the capillary force is sufficient to overcome the flow resistance of the working fluid. Therefore, one method of increasing the maximum thermal load is to reduce the flow resistance of the liquid and vapor with counter flow in the system. Moreover, the flow resistance of the working fluid is immediately dependent on the mass flow rate, and reducing the flow rate can effectively increase the maximum thermal load. The liquid bypass technique is one method of alleviating the flow resistance of the working fluid inner side a heat pipe container. In this work, a modified heat pipe system with one liquid bypass tube was manufactured and investigated, with the bypass tube being constructed so that some of the working fluid inside the condenser could be bypassed to an evaporator not going through a heat pipe interspace with vapor and liquid counterflow. Three bypass ports were located in the condenser; hence, the influence of bypass port area on thermal of heat pipe performance was investigated experimentally. Mass flow rate control valves were attached to these three bypass ports, and the maximum thermal loads according to the activation of each port were experimentally measured. The maximum thermal load in a horizontal position increased by up to 45.8% with an increase in the area of the bypass port. With the increase of the activated bypass port area, the condenser wall temperature increased by up to 15.9 °C.

Differentiation of primary central nervous system lymphoma from glioblastoma using optical coherence tomography based on attention ResNet.

.Significance: Differentiation of primary central nervous system lymphoma from glioblastoma is clinically crucial to minimize the risk of treatments, but current imaging modalities often misclassify glioblastoma and lymphoma. Therefore, there is a need for methods to achieve high differentiation power intraoperatively.Aim: The aim is to develop and corroborate a method of classifying normal brain tissue, glioblastoma, and lymphoma using optical coherence tomography with deep learning algorithm in an ex vivo experimental design.Approach: We collected tumor specimens from ordinal surgical operations and measured them with optical coherence tomography. An attention ResNet deep learning model was utilized to differentiate glioblastoma and lymphoma from normal brain tissues.Results: Our model demonstrated a robust classification power of detecting tumoral tissues from normal tissues and moderate discrimination between lymphoma and glioblastoma. Moreover, our results showed good consistency with the previous histological findings in the pathological manifestation of lymphoma, and this could be important from the aspect of future clinical practice.Conclusion: We proposed and demonstrated a quantitative approach to distinguish different brain tumor types. Using our method, both neoplasms can be identified and classified with high accuracy. Hopefully, the proposed method can finally assist surgeons with decision-making intraoperatively.

Optimal Clustering in Stable Instances Using Combinations of Exact and Noisy Ordinal Queries

This work studies clustering algorithms which operates with ordinal or comparison-based queries (operations), a situation that arises in many active-learning applications where “dissimilarities” between data points are evaluated by humans. Typically, exact answers are costly (or difficult to obtain in large amounts) while possibly erroneous answers have low cost. Motivated by these considerations, we study algorithms with non-trivial trade-offs between the number of exact (high-cost) operations and noisy (low-cost) operations with provable performance guarantees. Specifically, we study a class of polynomial-time graph-based clustering algorithms (termed Single-Linkage) which are widely used in practice and that guarantee exact solutions for stable instances in several clustering problems (these problems are NP-hard in the worst case). We provide several variants of these algorithms using ordinal operations and, in particular, non-trivial trade-offs between the number of high-cost and low-cost operations that are used. Our algorithms still guarantee exact solutions for stable instances of k-medoids clustering, and they use a rather small number of high-cost operations, without increasing the low-cost operations too much.

Algorithm for the formation of a linguistic integrated assessment of resource sustainability of an enterprise

The paper proposes an algorithm for the formation of a linguistic integrated assessment of the resource sustainability of an enterprise, based on the theory of extensive and intensive use of resources and methods of aggregating linguistic information using linguistic ordinal operators that formalize sequential averaging strategies for multicriteria estimation. The assessment of the extent of extensive and intensive use of resources in the work is carried out through groups of models that re ect the dependence of the resulting indicators of the enterprise on the quantity and quality of resources of various types. Quantitative indicators of the intensity of resource use are estimated by the method of chain substitutions; the Harrington function is used to switch to linguistic values. The integrated linguistic assessment obtained as a result of the work of the considered algorithm aggregates the linguistic values of the resource use intensity by all models and is interpreted as an integral indicator of resource stability, which is achieved due to intensive production factors.

Sterling stirling play

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set $$\left[ n\right] $$ . We call this ruleset Stirling Shave. A procedure utilizing the ordinal sum operation is given to determine the nim value of a given normal play position. Additionally, we enumerate the number of permutations of $$\left[ n\right] $$ which are $$\mathcal {P}$$ -positions. The formula given involves the Stirling numbers of the first-kind. We also give a complete analysis of the Misere version of Stirling Shave using Conway’s genus theory. An interesting by-product of this analysis is insight into how the ordinal sum operation behaves in Misere Play.

Using mesh hernioplasty to patient with inguinal Hernia

To clinically evaluate the outcome of Inguinal Hernioplasty in terms of haematoma, wound infection and recurrence, with special reference to surgery done by trainee surgeons. A total of 50 patients with inguinal hernia were operated during the study period. The result of the present study concluded that using mesh for surgical operation of hernia is much better than the ordinal operation of hernia because this technique reduces the recurrence of the disease, while the classical operation is related to recurrence of the disease. Also Mesh can reduce the appearing of hematomas, Wound infections after the operation, while the classical operation is related to appearing of the hematomas and Wound infections after the operation. Further more there is no significant difference between the two methods regarding appearing of seromas after the operation however, its appear among those patients which did a classical operation more than those which using mesh for operation. So In our set-up Mesh Hernioplasty has proven to be effective with low complication and recurrence rates.

Modelling multicriteria value interactions with Reasoning Maps

Idiographic causal maps are extensively employed in Operational Research to support problem structuring and complex decision making processes. They model means-end or causal discourses as a network of concepts connected by links denoting influence, thus enabling the representation of chains of arguments made by decision-makers. There have been proposals to employ such structures to support the structuring of multicriteria evaluation models, within an additive value measurement framework. However, a drawback of this multi-methodological modelling is the loss of richness of interactions along the means-end chains when evaluating options. This has led to the development of methods that make use of the structure of the map itself to evaluate options, such as the Reasoning Maps method, which employs ordinal scales and ordinal operators for such evaluation. However, despite their potential, Reasoning Maps cannot model explicitly value interactions nor perform a quantitative ranking of options, limiting their applicability and usefulness. In this article we propose extending the Reasoning Maps approach through a multilinear evaluation model structure, built with the MACBETH multicriteria method. The model explicitly captures the value interactions between concepts along the map and employs the MACBETH protocol of questioning to assess the strength of influence for each means-end link. The feasibility of the proposed approach to evaluate options and to deal with multicriteria interactions is tested in a real-world application to support the construction of a population health index.

자치단체의 독서진흥조례 내용분석

The purpose of this study is to investigate and analyze present condition of enactment and enforcement of regulation for reading culture promotion which is a local statute of the autonomous community of Korea to suggest effective improvement methods for operation of ordinance and regulation. In this research, literature review and regulation analysis were conducted and investigated. The results of this study are as follows. 1) There were 77 ordinances of reading related local statutes of 245 metropolitan and primary local authority and 7 regulations. 2) Ordinances and ordinance regulation of the local government and local government of education are being named variously. 3) Composition of ordinances ordinance regulation were not systematic due to diverse contents of ordinance by local government according to the names of ordinance, and they overlapped with similar contents in general. 4) There were 10 ordinances and 2 official orders for the abolished reading related local statutes of the local government until today. This study suggested the following methods to vitalize the reading culture promotion policy. 1) It would be necessary to improve awareness by promoting the reading promotion policy. 2) Optimal name for local statute and ordinance that considered the environment of reading promotion of local statue need to be assigned, and contents of the ordinance regulation related to reading needs to be consistent. 3) Local statutes need to be established by collecting enough opinions of residents or specialists after thoroughly examining problems of the ordinance before abolition.

Ordinal operations on graph representations of sets

AbstractAny set x is uniquely specified by the graph of the membership relation on the set obtained by adjoining x to the transitive closure of x. Thus any operation on sets can be looked at as an operation on these graphs. We look at the operations of ordinal arithmetic of sets in this light. This turns out to be simplest for a modified ordinal arithmetic based on the Zermelo ordinals, instead of the usual von Neumann ordinals. In this arithmetic, addition of sets corresponds to concatenating graphs, and multiplication corresponds to replacing each edge of a graph by a copy of another graph. Characterizations for the von Neumann case are also given.

Aggregation of ordinal information

Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.

A partition relation for successors of Large Cardinals

We address partition problems of Erdos and Hajnal by showing that $\kappa^+\to(\kappa^2+1,\alpha)$ for all $\alpha<\kappa^+$ , if $\kappa^{<\kappa}=\kappa$ and $\kappa$ carries a $\kappa$ -dense ideal. If $\kappa$ is measurable we show that $\kappa^+\to(\alpha)^2_n$ for $n<\omega, \alpha<\Omega$ where $\Omega$ is a very large ordinal less than $\kappa^+$ that is closed under all primitive recursive ordinal operations.

The normal form of Borel sets. Part II: Borel sets of infinite rank

For each Borel set of reals of infinite rank A we obtain a “normal form” of A by finding a Borel set Ω such that A and Ω continuously reduce to each other. We do so by defining simple Borel operations which are homomorphic to the ω 1 first Veblen ordinal operations of base ω 1 required to compute the Wadge degree of a Borel set.

On the Comparisons of OWA Operators and Ordinal OWA Operators

In this paper, comparisons of OWA operators and ordinal OWA operators are carried out by using lattice theoretic methods. It is proved first that in both cases, the set of all aggregation operators forms a lattice, then the concept of positive valuation is used to measure the "orness" of aggregation operators and the structures of all such possible "orness" measures are determined.

A Safety Analysis of the ITER Superconducting Magnet System in Case of Loss of Vacuum in the ITER Cryostat

One of the safety analysis for superconducting magnet system in International Thermonuclear Experimental Reactor (ITER) was carried out. The ITER cryostat will hold many superconducting magnets, such as twenty toroidal field coils, a central solenoid coil, and seven poloidal coils. Loss of vacuum of the cryostat was considered as the worst assumption and a safety analysis of the magnets was examined when the assumption would occur. Accordingly, the loss of vacuum will cause the loss of thermal shield vacuum for the magnets and then a large heat transfer will be generated in the cryostat. The magnet pressure and temperature will rise, bringing the magnets to quench. Such behavior was simulated by using a developed computer-aided calculation code. As a result of the calculation, a catastrophic phenomenon doesn`t appear in the assumption. It is observed that a quasi-stable state, where the magnet temperature is kept to less than 7 K, is maintained for more than 600 seconds. Thus, the magnet current can be slowly discharged as in ordinal operation without magnet quench even in such worst assumption due to the large volume of the cryostat. 3 refs., 3 figs., 1 tab.

Ordinal Operations on Surreal Numbers

An open problem posed by John H. Conway in [2] was whether one could, on his system of numbers and games, ‘… define operations of addition and multiplication which will restrict on the ordinals to give their usual operations’. Such a definition for addition was later given in [4], and this paper will show that a definition also exists for multiplication. An ordinal exponentiation operation is also considered.

Positive ∑ operations on ordinals and normal filters on greatly mahlo cardinals

If ℱ is a normal filter on a regular uncountable cardinal κ, let ║f║ be the ℱ-norm of an ordinal function f. We introduce the class of positive ordinal operations and prove that if F is a positive operation then ║F(f)║ ≥ F(║f║). For each η &lt; κ+ let fη be the canonical ηth function. We show that if F is a ∑ operation then F(fη) = fF(η).As an application we show that if κ is greatly Mahlo then there are normal filters on κ of order greater than κ+.

Measuring the Ordination→Cardination Sequence

During the short interval since the ordination+cardination sequence was reported, it has prompted a large amount of follow-up research. Interest in the sequence stems from the fact that, first, it is inconsistent with the prevailing view among educators that children's numerical concepts are basically cardinal (1, Ch. XI) and, second, it is inconsistent with predictions from Piaget's theory (1, ch. VI). Investigators who have conducted follow-up studies have devised some ingenious new procedures for measuring the ordination+cardination sequence (2, 3). Most of these new procedures seem valid. But, unfortunately, there is a problem with the method suggested by Williams (4, 5). The problem lies in Williams' definition of ordination. He claims that the key attribute of ordination is that it involves determination of number by Accually, counting is quite irrelevant to the logical definition of ordinal number (e.g., 1, Ch. 111) and, hence, it is irrelevant to ordination (which is the behavioral counterpart of ordinal number). Although counting may be used to generate instances of ordination, there are many other such instances that do not involve counting. It is important for researchers interested in number development to realize that counting is both an ordinal and a cardinal operation. In its most basic sense, counting is simply a method of correlating number names with objects. If Ss know that a certain number name, e.g., four, has a certain positional meaning (fourth), we have an example of ordination. If Ss know that a certain number name, e.g., four, has a certain numerousness meaning (quartet), we have an example of cardination. Finally, if Ss usually know positional meanings of number names before they know numerousness meanings, this might be viewed as an example of the underlying ordination+cardination sequence. In contrast, Williams examined Ss' tendency to conserve cardinal equivalence when they are allowed co count after transformation. Correct counting without subsequent conservation was viewed as an example of ordination+cardination. But, in line with wl~at I said about counting being a cardinal as well as an ordinal operation, note that the meanings of the number names generated in this situation are entirely cardinal, i.e., they always refer to numerousness and never to position. Therefore, it seems likely that the sequence Williams observed is not an example of ordination+cardination but, rather, is a novel sequence between earlier and later versions of cardination. This, at least, would be my interpretation.

Functionals defined by transfinite recursion

This paper deals mainly with quantifier-free second order systems (i.e., with free variables for numbers and functions, and constants for numbers, functions, and functionals) whose basic rules are those of primitive recursive arithmetic together with definition of functionals by primitive recursion and explicit definition. Precise descriptions are given in §2. The additional rules have the form of definition by transfinite recursion up to some ordinal ξ (where ξ is represented by a primitive recursive (p.r.) ordering). In §3 we discuss some elementary closure properties (under rules of inference and definition) of systems with recursion up to ξ. Let Rξ denote (temporarily) the system with recursion up to ξ. The main results of this paper are of two sorts:Sections 5–7 are concerned with less elementary closure properties of the systems Rξ. Namely, we show that certain classes of functional equations in Rη can be solved in Rη for some explicitly determined η &lt; ε(η) (the least ε-number &gt; ξ). The classes of functional equations considered all have roughly the form of definition by recursion on the partial ordering of unsecured sequences of a given functional F, or on some ordering which is obtained from this by simple ordinal operations. The key lemma (Theorem 1) needed for the reduction of these equations to transfinite recursion is simply a sharpening of the Brouwer-Kleene idea.

FOOD AND DRUGS

Report of Committee on Uniform Standard Milk Ordinance, Conference of State and Territorial Health Officers, 1926-A committee of 4 members, appointed by the 1925 Conference of State and Territorial Health Officers, was instructed to make a careful study of the so-called standard milk ordinance of the United States Public Health Service and submit a* report to the 1926 conference. The committee report comments on the advocacy of the so-called standard milk ordinance by the Public Health Service and is in accord with the general conclusions reached by Leslie C. Frank, Sanitary Engineer of the United States Public Health Service, in his paper presented at the American Health Congress at Atlantic City. The committee recommends, among other requirements, a provision in the standard milk ordinance for four grades of milk-Grade A pasteurized, Grade B pasteurized, Grade C pasteurized, and Grade A raw milk. The committee made inquiries of each of the 10 states in which the so-called standard milk ordinance has already been adopted and the report from each one of these states is that the operation of the ordinance is satisfactory and only one modification was suggested, i.e., that it should be made more adaptable to smaller communities which do not have laboratories. It is believed that the ordinance is so framed as to be attractive to the majority of types of cities, noting, however, that in none of the states in which it has been adopted is there a city of 500,000 population or over. Whether the ordinance will prove attractive to the larger cities, suggestion is made that the principal problem with which the state officials have to deal is not that of the largest cities, since in general these have inaugurated milk sanitary laws equal if not better than the average in the state as a whole. About 40 proposed modifications of the ordinance were submitted.to the committee which reports that with few exceptions none of them will affect the operation of the standard ordinance or lead to disagreement. Modifications which the committee feels may lead to disagreement are: The proposed modifications in reference to the pasteurization temperature. The committee reconumends that the ordinance should retain the pasteurization temperature of 1450 C. and not 142° as proposed. The second modification is the proposal that chlorine sterilization should be accepted as being as effective as sterilization with steam. The committee believes that this has not been proven and as the issue is a debatable one it would be wise to exclude this modification. The third modification is the proposal to accept the reductase test in place of the bacterial count. The committee feels this is another debatable issue and recommends that the proposed modification be included in the standard ordinance and that the states and cities opposing it may exclude it as a local adaptation of the ordinance. The committee, in conclusion, points out that the standard ordinance enjoins "minimum requirements"' and recommends its adoption, modified as suggested, by the Conference of State and Territorial Health Officers.-Puib. Health, Rep., 41:31, 1573, July 30, 1926.