A new conservation result of WKL 0 over RCA 0

2002 ◽  
Vol 41 (1) ◽  
pp. 55-63 ◽  
Author(s):  
António Marques Fernandes
Keyword(s):  
Conservation Result

A Buchholz derivation system for the ordinal analysis of KP + Π3-reflection

2006 ◽  
Vol 71 (4) ◽  
pp. 1237-1283
Author(s):  
Markus Michelbrink
Keyword(s):  
Ordinal Analysis ◽  
Notation System ◽  
Recursive Functions ◽  
Conservation Result ◽  
Ordinal Notation

AbstractIn this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Π3-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis of KP + Π3-Reflection. The method used is an extension of techniques developed by Wilfried Buchholz, namely operator controlled notation systems for RS∞-derivations. Similarly to Buchholz we obtain a characterisation of the provably recursive functions of KP + Π3-Reflection as <-recursive functions where < is the ordering on Rathjen's ordinal notation system . Further we show a conservation result for -sentences.

Wave Problems for Repetitive Structures and Symplectic Mathematics

1992 ◽  
Vol 206 (6) ◽  
pp. 371-379 ◽  
Author(s):  
W X Zhong ◽  
F W Williams
Keyword(s):  
Wave Scattering ◽  
Power Flow ◽  
Turbine Blades ◽  
Expansion Method ◽  
Space Structures ◽  
Scattering Problems ◽  
Symplectic Matrix ◽  
Conservation Result ◽  
Wave Problems ◽  
Chain Type

Based on the analogy between structural mechanics and optimal control theory, the eigensolutions of a symplectic matrix, the adjoint symplectic ortho-normalization relation and the eigenvector expansion method are introduced into the wave propagation theory for sub-structural chain-type structures, such as space structures, composite material and turbine blades. The positive and reverse algebraic Riccati equations are derived, for which the solution matrices are closely related to the power flow along the sub-structural chain. The power flow orthogonality relation for various eigenvectors is proved, and the energy conservation result is also proved for wave scattering problems.

scholarly journals Implementation of total productive maintenance (TPM) to increase overall equipment efficiency of an hotel industry

2018 ◽  
Vol 144 ◽  
pp. 05004 ◽  
Author(s):  
B. Manjunatha ◽  
T. R. Srinivas ◽  
C. G. Ramachandra
Keyword(s):  
Energy Conservation ◽  
Energy Saving ◽  
Hotel Industry ◽  
Direct Impact ◽  
Total Productive Maintenance ◽  
Good Source ◽  
Indian Economy ◽  
Electrical Systems ◽  
Public Areas ◽  
Conservation Result

Hotel industries are one of the fastest growing areas in India, which is attracting more number of jobs & tourists. This also results in direct impact on Indian economy. All Hotels comprises a higher element of total working cost and they are a good source of income. Hospitality is one of the most important components of hotel industry. To give a good hospitality in hotels to customers, we need to use different machines in different departments. For example if we take section of housekeeping it consists of different sub departments like Rooms & corridors, Toilets, Linen, Furniture and furnishings, Gardens, Public areas etc. In this connection a small implementation of TPM tool called focused improvement & planned maintenance, implemented in alternative usage of electrical systems (energy conservation). Result showed a very significant improvement in energy saving. By adopting Small changes show a significant improvement in the overall system. It also indicates the dire need of proper industrial tools in hotels. Total Productive Maintenance (TPM) is one of the pioneering approaches which can be achieved in above said things [1][2].

scholarly journals NUMERICAL CALCULATION ON SHORELINE CONSERVATION IN MAJURO ATOLL, THE MARSHALL ISLANDS

2011 ◽  
Vol 1 (32) ◽  
pp. 94 ◽  
Author(s):  
Daisaku Sato ◽  
Hiromune Yokoki
Keyword(s):  
Morphological Changes ◽  
Beach Nourishment ◽  
Marshall Islands ◽  
Island Conservation ◽  
Severe Erosion ◽  
Effective Option ◽  
Conservation Result ◽  
Conservation Plan ◽  
Erosion And Accretion ◽  
Erosion Volume

Development of a numerical model for future estimation of morphological changes in Majuro atoll were carried out, and, at the same time, examination of beach nourishment for sustainable island conservation plan was examined by the developed model. Identified erosion and accretion area from calculated shoreline indicated that the northern tip of Laura and some areas in LongIsland had severe erosion until 100 years later as well as large accretion in northern part of the atoll. Three beach nourishment scenarios using eroded sediments, which were accreted in deep lagoon in northern part of atoll, were examined and they decreased 30% of accumulative erosion volume compared with the non-conservation result. This result shows that the beach nourishment is an effective option to sustainable island conservation plan in Majuro atoll.

Syntactic translations and provably recursive functions

1985 ◽  
Vol 50 (3) ◽  
pp. 682-688 ◽  
Author(s):  
Daniel Leivant
Keyword(s):  
Cut Elimination ◽  
Mathematical Apparatus ◽  
Constructive Logic ◽  
Similar Nature ◽  
Recursive Functions ◽  
Conservation Result ◽  
Mathematical Techniques ◽  
Primitive Recursive ◽  
Potential Objection ◽  
Intuitionistic Version

Syntactic translations of classical logic C into intuitionistic logic I are well known (see [Kol25], [Gli29], [Göd32], [Kre58b], [M063], [Cel69] and [Lei71]). Harvey Friedman [Fri78] used a translation of a similar nature, from I into itself, to reprove a theorem of Kreisel [Kre58a] that various theories based on I are closed under Markov's rule: if ¬¬∃x.α is a theorem, where x is a numeric variable and α is a primitive recursive relation, then ∃x.α is a theorem. Composing this with Gödel's translation from classical to intuitionistic theories, it follows that the functions provably recursive in the classical version of the theories considered are provably recursive already in their intuitionistic version. This conservation result is important in that it guarantees that no information about the convergence of recursive functions is lost when proofs are restricted to constructive logic, thus removing a potential objection to the use of constructive logic in reasoning about programs (see [C078] for example). Conversely, no objection can be raised by intuitionists to proofs of formulas that use classical reasoning, because such proofs can be converted to constructive proofs (this has been exploited extensively; see [Smo82]).Proofs of closure under Markov's rule had required, until Friedman's proof, a relatively sophisticated mathematical apparatus. The chief method used Godel's “Dialectica” interpretation (see [Tro73, §3]). Other proofs used cut-elimination, provable reflection for subsystems [Gir73], and Kripke models [Smo73]. Moreover, adapting these proofs to new theories had required that the underlying meta-mathematical techniques be adapted first, not always a trivial step.

Witnessing functions in bounded arithmetic and search problems

1998 ◽  
Vol 63 (3) ◽  
pp. 1095-1115 ◽  
Author(s):  
Mario Chiari ◽  
Jan Krajíček
Keyword(s):  
Partial Order ◽  
Polynomial Time ◽  
Bounded Arithmetic ◽  
Pigeonhole Principle ◽  
Search Problems ◽  
Strict Partial Order ◽  
Conservation Result ◽  
Time Structures

AbstractWe investigate the possibility to characterize (multi)functions that are-definable with smalli(i= 1, 2, 3) in fragments of bounded arithmeticT2in terms of natural search problems defined over polynomial-time structures. We obtain the following results:(1) A reformulation of known characterizations of (multi)functions that areand-definable in the theoriesand.(2) New characterizations of (multi)functions that areand-definable in the theory.(3) A new non-conservation result: the theoryis not-conservative over the theory.To prove that the theoryis not-conservative over the theory, we present two examples of a-principle separating the two theories:(a) the weak pigeonhole principle WPHP(a2,f, g) formalizing that no functionfis a bijection betweena2andawith the inverseg,(b) the iteration principle Iter(a, R, f) formalizing that no functionfdefined on a strict partial order ({0,…, a},R) can have increasing iterates.

scholarly journals Transient Burning Rate Model for Solid Rocket Motor Internal Ballistic Simulations

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
David R. Greatrix
Keyword(s):  
Burning Rate ◽  
Solid Phase ◽  
Burning Surface ◽  
Solid Rocket Motor ◽  
Principal Mechanism ◽  
Conservation Result ◽  
Burning Model ◽  
Solid Rocket ◽  
Transient Burning Rate ◽  
Experimental Firing

A general numerical model based on the Zeldovich-Novozhilov solid-phase energy conservation result for unsteady solid-propellant burning is presented in this paper. Unlike past models, the integrated temperature distribution in the solid phase is utilized directly for estimating instantaneous burning rate (rather than the thermal gradient at the burning surface). The burning model is general in the sense that the model may be incorporated for various propellant burning-rate mechanisms. Given the availability of pressure-related experimental data in the open literature, varying static pressure is the principal mechanism of interest in this study. The example predicted results presented in this paper are to a substantial extent consistent with the corresponding experimental firing response data.

scholarly journals Opportunities drive the global distribution of protected areas

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e2989 ◽  
Author(s):  
Germán Baldi ◽  
Marcos Texeira ◽  
Osvaldo A. Martin ◽  
H. Ricardo Grau ◽  
Esteban G. Jobbágy
Keyword(s):  
Protected Areas ◽  
Variable Importance ◽  
Land Conservation ◽  
Sub Saharan Africa ◽  
Global Level ◽  
International Borders ◽  
Conservation Result ◽  
Preference Criteria ◽  
Sub Saharan ◽  
Environmental Representativeness

BackgroundProtected areas, regarded today as a cornerstone of nature conservation, result from an array of multiple motivations and opportunities. We explored at global and regional levels the current distribution of protected areas along biophysical, human, and biological gradients, and assessed to what extent protection has pursued (i) a balanced representation of biophysical environments, (ii) a set of preferred conditions (biological, spiritual, economic, or geopolitical), or (iii) existing opportunities for conservation regardless of any representation or preference criteria.MethodsWe used histograms to describe the distribution of terrestrial protected areas along biophysical, human, and biological independent gradients and linear and non-linear regression and correlation analyses to describe the sign, shape, and strength of the relationships. We used a random forest analysis to rank the importance of different variables related to conservation preferences and opportunity drivers, and an evenness metric to quantify representativeness.ResultsWe find that protection at a global level is primarily driven by the opportunities provided by isolation and a low population density (variable importance = 34.6 and 19.9, respectively). Preferences play a secondary role, with a bias towards tourism attractiveness and proximity to international borders (variable importance = 12.7 and 3.4, respectively). Opportunities shape protection strongly in “North America & Australia–NZ” and “Latin America & Caribbean,” while the importance of the representativeness of biophysical environments is higher in “Sub-Saharan Africa” (1.3 times the average of other regions).DiscussionEnvironmental representativeness and biodiversity protection are top priorities in land conservation agendas. However, our results suggest that they have been minor players driving current protection at both global and regional levels. Attempts to increase their relevance will necessarily have to recognize the predominant opportunistic nature that the establishment of protected areas has had until present times.

On universes in type theory

1998 ◽  
Author(s):  
Erik Palmgren
Keyword(s):  
Type Theory ◽  
Second Order ◽  
Separation Axiom ◽  
Second Order Arithmetic ◽  
Constructive Type Theory ◽  
Constructive Type ◽  
Early Results ◽  
Conservation Result ◽  
Constructive Set Theory ◽  
Order Arithmetic

The notion of a universe of types was introduced into constructive type theory by Martin-Löf (1975). According to the propositions-as-types principle inherent in type theory, the notion plays two roles. The first is as a collection of sets or types closed under certain type constructions. The second is as a set of constructively given infinitary formulas. In this paper we discuss the notion of universe in type theory and suggest and study some useful extensions. We assume familiarity with type theory as presented in, for example, Martin-Löf (1984). Universes have been effective in expanding the realm of constructivism. One example is constructive category theory where type universes take the roles of Grothendieck universes of sets, in handling large categories. A more profound example is Aczel’s (1986) type-theoretic interpretation of constructive set theory (CZF). It is done by coding ϵ-diagrams into well-order types, with branching over an arbitrary type of the universe. The latter generality is crucial for interpreting the separation axiom. The introduction of universes and well-orders (W-types) in conjunction gives a great proof-theoretic strength. This has provided constructive justification of strong subsystems of second-order arithmetic studied by proof-theorists (see Griffor and Rathjen (1994) and Setzer (1993), and for some early results, see Palmgren (1992)). At present, it appears that the most easily justifiable way to increase the proof-theoretic strength of type theory is to introduce ever more powerful universe constructions. We will give two such extensions in this paper. Besides contributing to the understanding of subsystems of second-order arithmetic and pushing the limits of inductive definability, such constructions provide intuitionistic analogues of large cardinals (Rathjen et al, in press). A third new use of universes is to facilitate the incorporation of classical reasoning into constructive type theory. We introduce a universe of classical propositions and prove a conservation result for ‘Π-formulas’. Extracting programs from classical proofs is then tractable within type theory. The next section gives an introduction to the notion of universe. The central part of the paper is section 3 where we introduce a universe forming operator and a super universe closed under this operator.

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