scholarly journals Unification and mathematical explanation

2021 ◽  
Author(s):  
Robert Knowles
Keyword(s):  
Divide And Conquer ◽  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Mathematical Explanations ◽  
Enhanced Indispensability Argument ◽  
One Step ◽  
The Right

AbstractThis paper provides a sorely-needed evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For non-believers, it contributes to a divide-and-conquer strategy for showing that there are no such explanations in science. My discussion also undermines the appeal to unifying power in support of the enhanced indispensability argument.

scholarly journals Platonic Relations and Mathematical Explanations

2020 ◽  
Author(s):  
Robert Knowles
Keyword(s):  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Scientific Explanations ◽  
Turn On ◽  
Mathematical Explanations ◽  
Mathematical Platonism ◽  
Adequate Understanding ◽  
Enhanced Indispensability Argument

Abstract Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.

scholarly journals Mathematical explanation and indispensability

2018 ◽  
Vol 33 (2) ◽  
pp. 233 ◽  
Author(s):  
Susan Vineberg
Keyword(s):  
Causal Explanation ◽  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Mathematical Realism ◽  
Explanatory Role ◽  
Mathematical Objects ◽  
Scientific Explanations ◽  
Enhanced Indispensability Argument

This paper discusses Baker’s Enhanced Indispensability Argument (EIA) for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not support realism about mathematical objects.

Three-Component [1+1+1] Cyclopropanation with Ruthenium(II)

2018 ◽  
Author(s):  
Tanner C. Jankins ◽  
Robert R. Fayzullin ◽  
Eugene Khaskin
Keyword(s):  
Quaternary Carbon ◽  
Poor Control ◽  
One Step ◽  
Synthetic Routes ◽  
Mechanistic Investigations ◽  
Chiral Centers ◽  
Metal Catalyzed ◽  
The Right ◽  
Substituted Cyclopropanes

We report a one-step, Ru(II)-catalyzed cyclopropanation reaction that is conceptually different from the previously reported protocols that include Corey-Chaykovsky, Simmons-Smith, and metal catalyzed carbene attack on olefins. Under the current protocol, various alcohols are transformed into sulfone substituted cyclopropanes with excellent isolated yields and diastereoselectivities. This new reaction forms highly congested cyclopropane products with three new C–C bonds, three or two new chiral centers and one new quaternary carbon center. 22 examples of isolated substrates are given. Previously reported synthetic routes for similar substrates are all multi-step, linear routes that proceed with overall low yields and poor control of stereochemistry. Experimental mechanistic investigations suggest initial metal-catalyzed dehydrogenation of the alcohol substrate and catalyst independent stepwise attack of two equivalents of sulfone on the aldehyde under basic conditions. While the Ru(II) is only responsible for the initial dehydrogenation step, the rate of aldehyde formation is crucial to maintaining the right balance of intermediates needed to afford the cyclopropane product.

scholarly journals Surgical treatment for common hepatic aneurysm. Original one-step technique

Open Medicine ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 898-904
Author(s):  
Bruno Amato ◽  
Renato Patrone ◽  
Gennaro Quarto ◽  
Rita Compagna ◽  
Roberto Cirocchi ◽  
...  
Keyword(s):  
Surgical Treatment ◽  
Hepatic Artery ◽  
Distal Part ◽  
Intraoperative Ultrasound ◽  
Section Area ◽  
One Step ◽  
A New Technique ◽  
Open Surgical Treatment ◽  
The Right ◽  
Vascular Stapler

AbstractIntroductionHepatic artery aneurysms are rare, and their treatment represents a challenge for the surgeons.Materials and methodsA new technique is presented for common hepatic artery (CHA) aneurysm: it requires minimal vascular surgical dissection and only one linear vascular stapler is applied at the bottom of aneurysm. Aneurysm exclusion is easily obtained, which allowed retrograde thrombosis. Liver blood supply is ensured to the right and left hepatic artery, through the gastroduodenal artery, and can be previously monitored, with temporary clamping of the section area, by visual control, enzyme evaluation and intraoperative ultrasound examination. We reported an open surgical treatment, with simultaneous removal of hepatic and adrenal metastases, secondary to colon cancer.ResultsThe duration of vascular surgery was 30 min and did not involve complications. Postoperative controls confirmed the efficacy of the procedure.DiscussionThis original technique can be added to the various open and endovascular techniques so far described for the treatment of a CHA aneurysm. It is advisable as open surgery, mostly in case of associated pathologies.ConclusionsThe authors believe that this “one shot” technique by vascular staple of the distal part of CHA is minimally invasive and effective to obtain the exclusion of the aneurysm.

Mandatory desexing of dogs: one step in the right direction to reduce the risk of dog bite? A systematic review

2017 ◽  
Vol 23 (3) ◽  
pp. 212-218 ◽  
Author(s):  
Katina D'Onise ◽  
Susan Hazel ◽  
Charles Caraguel
Keyword(s):  
Systematic Review ◽  
Dog Bite ◽  
One Step ◽  
The Right

CRITICAL REVIEW OF EMULSION STABILITY AND CHARACTERIZATION TECHNIQUES IN OIL PROCESSING

2021 ◽  
pp. 1-36
Author(s):  
Vahideh Angardi ◽  
Ali Ettehadi ◽  
Özgün Yücel
Keyword(s):  
Separation Efficiency ◽  
Petroleum Industry ◽  
Cost Effective ◽  
Downstream Processing ◽  
Physical Factors ◽  
Comprehensive Review ◽  
Factors Affecting ◽  
Mathematical Explanations ◽  
The Stability ◽  
The Right

Abstract Effective separation of water and oil dispersions is considered a critical step in the determination of technical and economic success in the petroleum industry over the years. Moreover, a deeper understanding of the emulsification process and different affected parameters is essential for cost-effective oil production, transportation, and downstream processing. Numerous studies conducted on the concept of dispersion characterization indicate the importance of this concept, which deserves attention by the scientific community. Therefore, a comprehensive review study with critical analysis on significant concepts will help readers follow them easily. This study is a comprehensive review of the concept of dispersion characterization and conducted studies recently published. The main purposes of this review are to 1) Highlight flaws, 2) Outline gaps and weaknesses, 3) Address conflicts, 4) Prevent duplication of effort, 5) List factors affecting dispersion. It was found that the separation efficiency and stability of dispersions are affected by different chemical and physical factors. Factors affecting the stability of the emulsions have been studied in detail and will help to look for the right action to ensure stable emulsions. In addition, methods of ensuring stability, especially coalescence are highlighted, and coalescence mathematical explanations of phenomena are presented.

Single-shelf library-type Markov chains with infinitely many books

1977 ◽  
Vol 14 (02) ◽  
pp. 298-308 ◽  
Author(s):  
Peter R. Nelson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Natural Order ◽  
Order Book ◽  
Exit Boundary ◽  
One Step ◽  
Step Transition ◽  
The Right ◽  
Positive Recurrent

In a single-shelf library having infinitely many books B 1 , B 2 , …, the probability of selecting each book is assumed known. Books are removed one at a time and replaced in position k prior to the next removal. Books are moved either to the right or the left as is necessary to vacate position k. Those arrangements of books where after some finite position all the books are in natural order (book i occupies position i) are considered as states in an infinite Markov chain. When k > 1, we show that the chain can never be positive recurrent. When k = 1, we find the limits of ratios of one-step transition probabilities; and when k = 1 and the chain is transient, we find the Martin exit boundary.

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