A simple relationship between Buchholz's new system of ordinal notations and Takeuti's system of ordinal diagrams

1987 ◽  
Vol 52 (3) ◽  
pp. 577-581 ◽  
Author(s):  
Mitsuhiro Okada
Keyword(s):  
Original System ◽  
Simple Relationship ◽  
Ordered Sets ◽  
Two Systems ◽  
Ordinal Notations ◽  
New System

Buchholz [4] simplified the system of ordinal notations of the Schütte school (cf. [12]), by using the notion of collapsing functions (cf. [5]). In this paper we give a simple relationship between Buchholz's new system of ordinal notations and Takeuti's system of ordinal diagrams. From this simple relationship it turns out that the structures of these two systems are very close.We give two systems OT(I) (§1) and OT(I, A) (§2) of ordinal notations which are considered generalizations of Buchholz's original system, where I and A are well-ordered sets. The original system OT of Buchholz [4] is OT(ω + 1, {0}) in our sense. Here the set OT(I) of ordinal notations is defined as a subset of the set Od(I) of ordinal diagrams in [6], and the set OT(I, A) of ordinal notations as a subset of the set O(I, A) of ordinal diagrams in [14].

scholarly journals Automatic Course Scheduling System in Universities Based on Hybrid Genetic-Ant Colony Algorithm

2021 ◽  
Vol 2066 (1) ◽  
pp. 012079
Author(s):  
Yanbei Duan ◽  
Wenjie Lu
Keyword(s):  
Hybrid Algorithm ◽  
Ant Colony Algorithm ◽  
Operation Time ◽  
Original System ◽  
Colleges And Universities ◽  
Ant Colony ◽  
Scheduling System ◽  
Course Scheduling ◽  
System A ◽  
New System

Abstract Scheduling is the daily work of the Ministry of Education in Colleges and universities. In the past ten years, the scale of our colleges and universities has expanded rapidly, but the teaching resources are relatively limited. Many schools are facing the problem of insufficient classroom resources and teachers resources. The current way of organizing courses is increasingly difficult to make full use of existing resources to solve the changing needs and inefficiencies, which need to be improved urgently. This paper applies the hybrid Genetic-Ant algorithm to the automatic course scheduling system in Colleges and universities, and uses the cross-function to design and build the automatic course scheduling system in Colleges and universities. And select a college’s course scheduling system from this city for research, and use the Genetic-Ant hybrid algorithm to improve the original system to form a new system, called the original system A, and called the improved new system B, to compare the operation time and system suitability of the two systems. The results show that the fitness of system B is better than that of system A. When the scheduling unit is 100, the fitness of system A is 181, and system B is 203. When the scheduling unit is 400, the fitness of system B is 14 higher than that of system A. When the scheduling unit is 800, the fitness of system B is 64 higher than that of system A. Thus, the hybrid algorithm of genetic ant colony can improve the rationality of the curriculum.

The Rise of Academic Innovationism

2018 ◽  
pp. 79-115
Author(s):  
Steven Brint
Keyword(s):  
Research Universities ◽  
Knowledge Exchange ◽  
Reciprocal Relations ◽  
Academic Innovation ◽  
The Future ◽  
Two Systems ◽  
Research And Education ◽  
New System

This chapter discusses the analytical contrast between the two systems for organizing research and education, the system of academic professionalism and the system of academic innovationism. Under the impetus of academic innovationism, universities became more porous to the outside world and reciprocal relations of knowledge exchange grew denser. On balance, the new system contributed significantly and positively to the research prowess of universities. But it has also yielded a spotty record—some extraordinary successes but also many short-lived, troubled collaborations. Some universities invested heavily in the infrastructure to foster academic innovation and had little to show for their investments. For research universities, the challenge for the future will be to expand the possibilities to contribute more to the national innovation effort.

scholarly journals Studies in Qur’an and Hadith

1989 ◽  
Vol 6 (2) ◽  
pp. 329-335
Author(s):  
Muhammad Khalid Mas’ud
Keyword(s):  
Islamic Law ◽  
Early Period ◽  
Doctoral Dissertation ◽  
Central Theme ◽  
Early Islam ◽  
Two Systems ◽  
The Subject ◽  
Original Reading ◽  
New System ◽  
Husband And Wife

David S. Powers’ book, originally a doctoral dissertation submitted toPrinceton University, is a welcome addition to the already growing corpusof studies revising Joseph Schacht’s thesis that Islamic law did not exist duringthe lifetime of the Prophet. This is, however, not the central theme ofthe book. Powers contends that the Islamic law of inheritance is not identicalto the system of inheritance revealed to Prophet Muhammad and that theMuslim community is not in possession of the original reading and understandingof several Qur’anic verses and Prophetic hadith.The thesis presented in this book can be summarized as follows:Islamic law began to develop with Qur‘anic legislation which was moreclear and systematic on the subject of inheritance. In pre-Islamic Arabia theintergenemtional transmission of property was by seniority rather than by directdescent. The Qur’an introduced a new system of inheritance which reflecteda transition from tribalism to individualism, with more emphasis on the rightsof women to property. The author sees two systems of the law of inheritancein Islam:1) The proto-Islamic law of inheritance which existed only during2) Islamic law of inheritance, which exists as ‘ilm al-farii‘id.the lifetime of the Prophet; and,Powers contends that the proto-Islamic system was mainly testatory andthe property was distributed according to fixed shares only in the absenceof a will. Husband and wife, not being blood relatives, inherited as testatoryheirs.The author divides his dissertation into two parts. In the first part he dealswith the proto-Islamic, in the second with the Islamic system of inheritance.The first part proceeds by looking at the practice of bequest and testation inMakkah and Madinah in early Islam, giving special attention to the inheritancebetween husbands and wives, and the Qur’anic law of testation and intestacy.The second part proceeds by looking at socio-economic developmentsin the early period and contends that people in power manipulated the Qur‘anic ...

scholarly journals Physiological and Notational Comparison of New and Old Scoring Systems of Singles Matches in Men's Badminton

2011 ◽  
Vol 17 (1) ◽  
pp. 6-17 ◽  
Author(s):  
Hsin Lian CHEN ◽  
Chang Jun WU ◽  
Trevor C. CHEN
Keyword(s):  
Perceived Exertion ◽  
Physiological Responses ◽  
Scoring Systems ◽  
Physiological Data ◽  
Systematic Observation ◽  
Time Frequency ◽  
Two Systems ◽  
Playing Time ◽  
Lactate Levels ◽  
New System

LANGUAGE NOTE | Document text in English; abstract also in Chinese. This study compared the physiological responses and shot selection preferences of male singles players between thenew (rally-point) and old (scoring-by-service) scoring systems. Ten male athletes each played two matches against the same opponent on different days using the lottery method. Matches were notated using a systematic observation instrument, and physiological data were measured using heart rate (HR), ratings of perceived exertion (RPE) and blood lactate levels (LA). Results showed no differences in peak HR, RPE or LA responses between the two systems. However, players spent more time at an HR greater than 90%HRpeak under the old system (63%) than under the new system (54%). Notational analysis demonstrated a significant decrease in total match playing time (PT: 29 min), work time (10 min), work density (0.57), rest time (18 min), effective playing time (36%), number of rallies (203) and serves (35) under the new system as compared to the old system (e.g. PT: 42 min). No significant differences were noted between the two systems for number of shots, rally time, stroke time, frequency distribution of shot selection and positions during the matches, and for shot methods on the last shot of each rally. These findings suggest that the new system can significantly shorten PT compared to the old system, and that physiological responses, shot selection and positions do not affect between the systems. Meanwhile, the greater proportion of time spent at higher HR intensities under the old system may be attributed to the longer playing time with the opponent. 本研究目的，針對「新(落地得分)、舊制(發球得分)羽球單打比賽時之生理反應和擊球方式」做比較。以羽球正式比賽抽籤方式讓10位大學男子甲組羽球選手，決定其各二場新、舊制羽球單打比賽同一位對手之方式。以高速攝影機拍攝每場比賽做為系統性觀察法之內容分析，並在每場比賽時測驗心跳率 (HR)、運動自覺量表(RPE)和血乳酸濃度 (LA)做為生理反應的評估指標。結果顯示，羽球新、舊制比賽間引起心跳率峰值 (HRpeak)、RPE或血乳酸上升的反應並無統計差異。然而，舊制比賽時>90%HRpeak強度的比率(63%)明顯比新制 (54%)來得多。新制比賽的整場比賽完成時間 (PT：29分鐘)、淨比賽時間 (10分鐘)、運動密度 (0.57)、休息時間 (18分鐘)、比賽時間效益 (36%)、每球來回完成次數 (203)及發球次數 (35)都明顯比舊制 (例 如PT：42分鐘)縮短，但二種不同比賽間在揮拍次數、每球來回完成時間、擊球時間、擊球方式、擊球位置及每球最後一拍的擊球方式均無統計差異。這些結果顯示，新賽制規則改變會比舊賽制明顯縮短比賽時間，但不同賽制間所引起的生理反應、擊球方式及位置則不因規則改變而受到影響。此外，舊賽制比新賽制出現較高心跳率分佈情形，可歸因於舊制比賽之雙方選手有較多對抗機會或較長比賽時間所造成的。

Combined Supercharging System: The Best Fit for Submarine Engines

2001 ◽  
Author(s):  
R. Herrmann
Keyword(s):  
Test Bench ◽  
Specific Power ◽  
Two Stage ◽  
Pressure Stage ◽  
Classical Systems ◽  
Two Systems ◽  
High Pressure Stage ◽  
Low Sensitivity ◽  
Best Fit ◽  
New System

Abstract The two types of supercharging processes, either with turbocharger or with mechanically driven compressor are the two systems known to be used on diesel engines for submarines. Each of these two systems has its own limitations. A two stage supercharging system has been investigated and developed by S.E.M.T. Pielstick. This system is based on a turbocharger used as a low-pressure stage combined with a high-pressure stage compressor which is mechanically driven by the engine. Test bench results are compared with those obtained with the classical systems. The new system with two-stage compression has an advantage particularly for the following main points: - specific power, - air and fuel specific consumptions, - capability to sustain high exhaust back pressures as well as low suction pressures and low sensitivity to their fluctuations, - safety against engine stalling in case of loss of submersion control.

Constructing a Chaotic System with Any Number of Attractors

2017 ◽  
Vol 27 (08) ◽  
pp. 1750118 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Vector Field ◽  
Geometric Structure ◽  
Autonomous System ◽  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
Original System ◽  
Chaotic Attractors ◽  
Global Dynamics ◽  
The Basin Of Attraction ◽  
New System

Applying some transformation to an autonomous system, we obtain a new system, which might keep the dynamical behavior of the original system or generate different dynamics. But this is often accompanied by the appearance of discontinuous points, where the vector field for the new system is not continuous at these points. We discuss the effects of the discontinuous points, and provide two methods to construct systems with any preassigned number of chaotic attractors via some transformation. The first one does not change the geometric structure of the attractors, since the discontinuous points are out of the basin of attraction. The second one might make the new systems have different dynamics, like multiscroll chaotic attractors, or infinitely many chaotic attractors. These results illustrate that both the equilibria and the discontinuous points affect the global dynamics.

Effect of Local Modifications on the Vibration Characteristics of Linear Systems

1968 ◽  
Vol 35 (2) ◽  
pp. 327-332 ◽  
Author(s):  
J. T. Weissenburger
Keyword(s):  
Linear System ◽  
Eigenfunction Expansion ◽  
Natural Frequencies ◽  
Original System ◽  
Vibration Characteristics ◽  
Concentrated Mass ◽  
Linear Eigenvalue Problem ◽  
Local Modification ◽  
Linear Spring ◽  
New System

A method is presented for predicting the effect of a local modification such as the addition or removal of a concentrated mass or linear spring on the vibration characteristics of a linear system. The method, which is mathematically applicable to any linear eigenvalue problem, is rigorous even for large changes and has its basis in an eigenfunction expansion of the solution of the modified system in terms of the eigenfunctions of the unmodified system. Given the natural frequencies and modes of the original system, the characteristic function of the modified system is of such a form that it may be solved with a significant reduction in work as compared with direct treatment of the new system.

Emch's calculus and strict implication

1936 ◽  
Vol 1 (3) ◽  
pp. 77-86 ◽  
Author(s):  
C. I. Lewis
Keyword(s):  
Strict Implication ◽  
Logical Implication ◽  
Logical Consistency ◽  
Mathematical Properties ◽  
Logical Equivalence ◽  
System L ◽  
Two Systems ◽  
Formal Properties ◽  
New System

In a previous number of this Journal, Dr. Arnold F. Emch argues that the mathematical properties of the system of strict implication preclude the interpretation of p⊰q as synonymous with “q is deducible from p” and of ◊(pq), or p o q, as “p and q are consistent.” He proposes a new calculus of propositions in which the primitive ideas of the system of strict implication are retained but an additional idea, “logical consistency,” Op, is introduced, and two new relations, “logical implication,” p∾q, and “logical equivalence,” p = q, are denned. He believes that the properties of this new system are in accord with the facts about deducibility, consistency, and independence of propositions where those of p⊰q and ◊(pq) fail of such accord.Not all of the objections which Dr. Emch advances against strict implication are given due consideration in what follows. Concerning one especially important point, something will be said at the end of this paper. For the rest, discussion will here be limited to certain formal properties of the two systems, and certain consequences for the interpretation of them.For brevity, the system of strict implication will be referred to, in what follows, as the “system S,” or merely as S; and Dr. Emch's calculus as the “system L,” or as L.

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