The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones

The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.

Mathematical Definitions of Operators for Cartographic Generalization

This paper puts forword 11 cartographic generalization operator models and introduces their mathematical definitions,and thus a precise mathematical form and quantitative description has been given to these formerly limited qualitative concepts.The meaning of mathematical definition of operators for cartographic generalization and the application prospect in computer_aided cartography (CAC) is stated.ract The Jurassic strata in Jingyan of Sichuan containing the Mamenchinsaurus fauna are dealt with and divided in this paper. The Mamenchisaurus fossils contained there are compared in morphological features and stratigraphically with other types of the genus on by one. The comprehensive analysis show that the Mamenchisaurus fauna of Jingyan appeared in the early Late Jurassic and is primitive in morphology. The results of the morphological identification and stratigraphical study agree with each other. Their evolutionary processes in different apoches of the Late Jurassic also made clear. Key words Jingyan, Sichuan, Mamenchisaurus Fauna, stratigraphy, evolution

The International Study Group of Pancreatic Surgery definition of delayed gastric emptying and the effects of various surgical modifications on the occurrence of delayed gastric emptying after pancreatoduodenectomy

BACKGROUND:A number of definitions have been used for delayed gastric emptying(DGE) after pancreatoduodenectomy and the reported rates varied widely.The International Study Group of Pancreatic Surgery(ISGPS) definition is the current standard but it is not used universally.In this comprehensive review,we aimed to determine the acceptance rate of ISGPS definition of DGE,the incidence of DGE after pancreatoduodenectomy and the effect of various technical modifications on its incidence.DATA SOURCE:We searched PubM ed for studies regarding DGE after pancreatoduodenectomy that were published from 1 January 1980 to 1 July 2015 and extracted data on DGE definition,DGE rates and comparison of DGE rates among different technical modifications from all of the relevant articles.RESULTS:Out of 435 search results,178 were selected for data extraction.The ISGPS definition was used in 80% of the studies published since 2010 and the average rates of DGE and clinically relevant DGE were 27.7%(range:0-100%;median:18.7%) and 14.3%(range:1.8%-58.2%;median:13.6%),respectively.Pylorus preservation or retrocolic reconstruction were not associated with increased DGE rates.Although pyloric dilatation,Braun’s entero-enterostomy and Billroth Ⅱ reconstruction were associated with significantly lower DGE rates,pyloric ring resection appears to be most promising with favorable results in 7 out of 10 studies.CONCLUSIONS:ISGPS definition of DGE has been used in majority of studies published after 2010.Clinically relevant DGE rates remain high at 14.3% despite a number of proposed surgical modifications.Pyloric ring resection seems to offer the most promising solution to reduce the occurrence of DGE.

Circulation Indices of the Aleutian Low Pressure System:Definitions and Relationships to Climate Anomalies in the Northern Hemisphere

In this study, a group of indices were defined regarding intensity （P）, area （S） and central position （λc, Фc） of the Aleutian low （AL） in the Northern Hemisphere in winter, using seasonal and monthly mean height field at 1000-hPa. These indices were calculated over 60 winter seasons from 1948/1949 to 2007/2008 using reanalysis data. Climatic and anomalous characteristics of the AL were analyzed based on these indices and relationships between the AL, and general circulations were explored using correlations between indicesP, λc, and Pacific SST, as well as Northern Hemisphere temperature and precipitation. The main results are these： （1） AL is the strongest in January, when the center shifts to the south and west of its climatological position, and it is the weakest in December when the center shifts to the north and east. （2） AL intensity （P） is negatively correlated with its longitude （λc）： a deeper low occurs toward the east and a shallower low occurs toward the west. On a decadal scale, the AL has been persistently strong and has shifted eastward since the 1970s, but reversal signs have been observed in recent years. （3） The AL is stronger and is located toward the east during strong E1 Nifio winters and vice versa during strong La Nifia years; this tendency is particularly evident after 1975. The AL is also strongly correlated with SST in the North Pacific. It intensifies and moves eastward with negative SST anomalies, and it weakens and moves westward with positive SST anomalies. （4） Maps of significance correlation between AL intensity and Northern Hemisphere temperature and rainfall resemble the PNA teleconnection pattern in mid-latitudes in the North Pacific and across North America. The AL and the Mongolian High are two permanent atmospheric pressure systems adjacent to each other during boreal winter over the middle and high latitudes in the Northern Hemisphere, but their relationships with the E1 Nifio/La Nifia events and with temperature and precipitation in the Northern Hemisphere are significantly different.

A note on the definition of fractional derivatives applied in rheology

It is known that there exist obivious differences between the two most commonly used definitions of fractional derivatives-Riemann-Liouville （R-L） definition and Caputo definition. The multiple definitions of fractional derivatives in fractional calculus have hindered the application of fractional calculus in rheology. In this paper, we clarify that the R-L definition and Caputo definition are both rheologically imperfect with the help of mechanical analogues of the fractional element model （Scott-Blair model）. We also clarify that to make them perfect rheologically, the lower terminals of both definitions should be put to ∞. We further prove that the R-L definition with lower terminal a →∞ and the Caputo definition with lower terminal a →∞ are equivalent in the differentiation of functions that are smooth enough and functions that have finite number of singular points. Thus we can define the fractional derivatives in rheology as the R-L derivatives with lower terminal a →∞ （or, equivalently, the Caputo derivatives with lower terminal a →∞） not only for steady-state processes, but also for transient processes. Based on the above definition, the problems of composition rules of fractional operators and the initial conditions for fractional differential equations are discussed, respectively. As an example we study a fractional oscillator with Scott-Blair model and give an exact solution of this equation under given initial conditions.

Consensus on the definition of colorectal anastomotic leakage: A modified Delphi study

BACKGROUND Despite the emerging knowledge about colorectal anastomotic leakage(CAL)through the increasing number of clinical and experimental studies, there is no generally accepted definition of CAL. Because of the wide variety of definitions used in literature, comparison of study outcomes and quality of care is complicated.AIM To reach consensus on the definition of CAL using a modified Delphi method.METHODS The RAND/UCLA appropriateness method was used. The expert panel consisted of international colorectal surgeons and researchers who had published three or more articles about CAL. The consensus process consisted of two online distributed questionnaires and a third round with a recommendation. In the questionnaires participants were asked to rate the appropriateness of statements using a 1-9 Likert scale. Consensus was defined as a panel median between 1-3 or 7-9 without disagreement. In the final round a recommendation was formed regarding the definition of CAL and the expert panel was asked if they agreed or disagreed.RESULTSTwenty-three authors participated in the first round and twenty-one finished the second round. After two rounds consensus was reached on 37 items(80%) in nine different categories. The International Study Group of Rectal Cancer definition is the most frequently advised general definition by our panel. Consensus was reached regarding the clinical symptoms of CAL, which serum markers contributes to the suspicion of CAL, which radiological and perioperative findings should be considered as CAL, which grading system is appropriate and if there should be a range of postoperative days in the definition. Eventually, 19 experts completed all three rounds of which 16(84%) agreed with our final recommendations for the definition of CAL.CONCLUSION A consensus-based recommendation for the definition of CAL was formed using our modified Delphi method that can be widely incorporated in the field.

Impact of the Winter North Pacific Oscillation on the Surface Air Temperature over Eurasia and North America: Sensitivity to the Index Definition

This study analyzes the impact of the winter North Pacific Oscillation（NPO） on the surface air temperature（SAT）variations over Eurasia and North America based on six different NPO indices. Results show that the influences of the winter NPO on the SAT over Eurasia and North America are sensitive to the definition of the NPO index. The impact of the winter NPO on the SAT variations over Eurasia（North America） is significant（insignificant） when the anticyclonic anomaly associated with the NPO index over the North Pacific midlatitudes shifts westward and pronounced northerly wind anomalies appear around Lake Baikal. By contrast, the impact of the winter NPO on the SAT variations over Eurasia（North America）is insignificant（significant） when the anticyclonic anomaly over the North Pacific related to the NPO index shifts eastward and the associated northerly wind anomalies to its eastern flank extend to North America. The present study suggests that the NPO definition should be taken into account when analyzing the impact of the winter NPO on Eurasian and North American SAT variations.

Poorly cohesive cells gastric carcinoma including signet-ring cell cancer:Updated review of definition,classification and therapeutic management

While the incidence of gastric cancer(GC)in general has decreased worldwide in recent decades,the incidence of diffuse cancer historically comprising poorly cohesive cells-GC(PCC-GC)and including signet ring cell cancer is rising.Literature concerning PCC-GC is scarce and unclear,mostly due to a large variety of historically used definitions and classifications.Compared to other histological subtypes of GC,PCC-GC is nevertheless characterized by a distinct set of epidemiological,histological and clinical features which require a specific diagnostic and therapeutic approach.The aim of this review was to provide an update on the definition,classification and therapeutic strategies of PCC-GC.We focus on the updated histological definition of PCC-GC,along with its implications on future treatment strategies and study design.Also,specific considerations in the diagnostic management are discussed.Finally,the impact of some recent developments in the therapeutic management of GC in general such as the recently validated taxane-based regimens(5-Fluorouracil,leucovorin,oxaliplatin and docetaxel),the use of hyperthermic intraperitoneal chemotherapy as well as pressurized intraperitoneal aerosol chemotherapy and targeted therapy have been reviewed in depth for their relative importance for PCC-GC in particular.

On the Definition of Propellant Force

Comments are given on the various physical definitions of the force constant of propellant. As there are more or less defects in these definitions, two new definitions are presented to reflect the physical essence of propellant force more perfectly and could well compatible with the mathematical expression.

A mathematical model of symmetry based on mathematical definition

Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.

On the Definition of Life

The definition of life is a very important issue in the philosophy of biology,but this issue has unfortunately been neglected by the mainstream philosopher of biology for many years.In this paper,the difficulties with and the reasons for defining life are illustrated,the characteristics of life on Earth are explored,ways of defining life are examined,the main definitions of life are explained and evaluated,and finally,a new information definition of life is proposed.

Upgrading the definition of early gastric cancer: better staging means more appropriate treatment

Since Murakami defined early gastric cancer(EGC) as a "carcinoma limited to the gastric mucosa and/or submucosa regardless of the lymph node status", several authors have focused on the most influential histopathological parameters for predicting the development of lymph node metastases by considering the lymph node status as an important prognostic factor. A few authors have also considered the depth of invasion as one of the keys to explaining the existence of subgroups of patients affected by EGC with poor prognoses. In any case, EGC is still considered an initial phase of tumor progression with good prognosis. The introduction of modern endoscopic devices has allowed a precise diagnosis of early lesions, which can lead to improved definitions of tumors that can be radically treated with endoscopic mucosal resection or endoscopic submucosal dissection(ESD). Given the widespread use of these techniques, the Japanese Gastric Cancer Association( JGCA) identified in 2011 the standard criteria that should exclude the presence of lymph node metastases. At that time, EGCs with nodal involvement should have been asserted as no longer fitting the definition of an early tumor. Some authors have also demonstrated that the morphological growth pattern of a tumor, according to Kodama's classification, is one of the most important prognostic factors, thereby suggesting the need to report it in histopathological drafts. Notwithstanding the acquired knowledge regarding the clinical behavior of EGC, Murakami's definition is still being used. This definition needs to be upgraded according to the modern staging of the disease so that the appropriate treatment would be selected.

Effectiveness and safety of combined nimotuzumab and S-1 chemotherapy with concurrent radiotherapy for locally advanced esophageal cancer in malnourished and elderly patients:A prospective phaseⅡstudy

Objective:Definitive chemoradiotherapy(dCRT)is the standard treatment for unresectable locally advanced esophageal cancer.However,this treatment is associated with substantial toxicity,and most malnourished or elderly patients are unable to complete this therapy.Therefore,there is a need for a more suitable radiotherapy combination regimen for this population.This study was aimed to evaluate the efficacy and safety of a combination regimen comprising chemotherapy with nimotuzumab and S-1 and concurrent radiotherapy for patients with fragile locally advanced esophageal cancer with a high Nutritional Risk Screening 2002(NRS-2002)score.Methods:Eligible patients with unresectable esophageal carcinoma who had an NRS-2002 score of 2 or higher were enrolled.They were treated with S-1 and nimotuzumab with concurrent radiotherapy,followed by surgery or definitive radiotherapy.The primary endpoint was the locoregional control(LRC)rate.Results:A total of 55 patients who met the study criteria were enrolled.After completion of treatment,surgery was performed in 15 patients and radiotherapy was continued in 40 patients.The median follow-up period was 33.3[95%confidence interval(95%CI,31.4−35.1)]months.The LRC rate was 77.2%(95%CI,66.6%−89.4%)at 1 year in the entire population.The overall survival(OS)rate and event-free survival(EFS)rate were 57.5%and 51.5%at 3 years,respectively.Surgery was associated with better LRC[hazard ratio(HR)=0.16;95%CI,0.04−0.70;P=0.015],OS(HR=0.19;95%CI,0.04−0.80;P=0.024),and EFS(HR=0.25;95%CI,0.08−0.75;P=0.013).Most adverse events were of grade 1 or 2,and no severe adverse events occurred.Conclusions:For malnourished or elderly patients with locally advanced esophageal cancer,radiotherapy combined with nimotuzumab and S-1 is effective and has a good safety profile.

Considerations on the concept, definition, and diagnosis of amyotrophic lateral sclerosis

The concept, definition, and diagnosis of amyotrophic lateral sclerosis(ALS) currently present some problems. This article systematically reviews the literature on the history, current concepts, definition, and diagnosis of ALS, and discloses the present problems based on the retrieved literature and the authors' clinical experience. The current concepts and definitions of ALS have not yet been unified or standardized in clinical practice, and are sometimes vague or inaccurate, which can cause difficulties for neurologists in the clinical treatment of ALS. The concept and definition of ALS need to be further ascertained, and the current diagnostic criteria for ALS require further development. The identification of effective and objective biomarkers may be a feasible method for the early and accurate diagnosis of ALS. Therefore, future research should focus on the identification of reliable biomarkers—especially neuroimaging biomarkers—through autopsy. Standardizing the concept and definition of ALS and formulating clear diagnostic criteria will largely avoid many uncertainties in the future clinical research and treatment of ALS, which will greatly benefit patients.

An Equivalent Definition of the Crossed Cube

For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two vertices in it.

Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

Improving definition of the term “synchronous liver metastases” from colorectal cancer

The liver is the most frequent site of metastasis in colorectal cancer with up to a quarter of patients having liver metastases at the time of initial diagnosis and a further third subsequently developing liver lesions.Patients who present with metastatic liver disease after treatment of the primary(termed metachronous disease)receive care focused on this new metastatic disease.In contrast,the management of patients who present with colorectal cancer and concurrent liver

A Brief Introduction about the Definitions of Rhetoric

This paper classifies the definitions of rhetoric into four groups based on the defining methods in Li’s English Rhetoric and Essay Writing so that one can have a deeper understanding of the term "rhetoric".

Autonomic neurocardiogenic syndrome is stonewalled by the universal definition of myocardial infarction

Myocardial infarction(MI)is defined as myocardial cell death due to prolonged myocardial ischemia.Clinically,troponin rise and/or fall have become the“defining feature of MI”according to the universal definition of MI(UD-MI).Takotsubo syndrome(TS)and TS-related disease conditions also cause troponin elevation with typical rise and/or fall pattern but through a mechanism other than coronary ischemia.By strict application of the clinical diagnostic criteria for type-1 MI,type-2 MI,type-3 MI,and MI with non-obstructive coronary arteries according to the UD-MI including the fourth one published recently,TS and most of the 26 other causes of troponin elevation mentioned in the fourth UD-MI may erroneously be classified as MI.The existing evidence argues for the case that TS by itself is not a MI.Hyper-activation of the autonomic-sympathetic nervous system including local cardiac sympathetic hyper-activation and disruption with nor-epinephrine churn and spillover is the most probable cause of TS.This autonomic neuro-cardiogenic(ANCA)mechanism results in myocardial“cramp”(stunning),the severity and duration of which depend on the degree of the sympathetic-hyperactivation and nor-epinephrine spillover.The myocardial cramp may squeeze the cytosolic free troponin pools causing mild to moderate troponin elevation in TS and TS-related disease conditions.This ANCA syndrome,which has hitherto been enveloped by the UD-MI over more than one decade,may occur in acute,recurrent,and chronic forms.In this critical review,the controversies of UD-MI,evidence for ANCA syndrome,and a hypothetical mechanism for the troponin elevation in ANCA syndrome are provided.

On the definition of fractional derivatives in rheology

During the last two decades fractional calculus has been increasingly applied to physics, especially to rheology.It is well known that there are obivious differences between Riemann-Liouville (R-L) definition and Caputo definition,which are the two most commonly used definitions of fractional derivatives.The multiple definitions of fractional derivatives have hindered the application of fractional calculus in rheology.In this paper,we clarify that the R-L definition and Caputo definition are both Theologically unreasonable with the help of the mechanical analogues of the fractional element model.We also find that to make them more reasonable Theologically,the lower terminals of both definitions should be put to—∞.We further prove that the R-L definition with lower terminal—∞and the Caputo definition with lower terminal—∞are equivalent in the differentiation of functions that are smooth enough and functions that have finite number of singular points.Thus we can define the fractional derivatives in rheology as the R-L derivatives with lower terminal—∞(or,equivalently,the Caputo derivatives with lower terminal—∞) not only for steady-state processes,but also for transient processes.