Preliminary Identification of a Prime Number Other Than 2 and 3, the Origin of Twin Prime Numbers, the Structure of the Chain of Prime Numbers and the Set of Prime Numbers Less Than a Given Integer

The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it Esp. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted Enp. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted Ep. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.

Polynomial Functions Composed of Terms with Non-Integer Powers

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.

ESTIMATION OF THE CRITICAL RATE OF TEMPERATURE INCREASE OF THERMAL EXPLOSION OF NITROCELLULOSE USING NON-ISOTHERMAL DSC

A method of estimating the critical rate of temperature increase of thermal explosion for the first orderautocatalytic decomposition reaction system using non-isothermal DSC is presented. Information is obtained on theincreasing rate of temperature in nitrocellulose containing 13.54% of nitrogen when the first order autocatalytic decomposition converts into thermal explosion.

Symbol Error Rate Performance Analysis of Non-Orthogonal Multiple Access for Visible Light Communications

Non-orthogonal multiple access(NOMA) is considered as one of promising radio access techniques for visible light communications(VLC) in next-generation wireless communications systems.In order to provide theoretical support for designing VLC-NOMA,we derive its analytic expressions for the symbol error rate(SER).Specifically,NOMA is first incorporated with appropriate VLC to establish a VLC-NOMA framework.Afterwards,mathematical expressions of the SER for the VLC-NOMA are developed.Moreover,numerical results are provided carefully to demonstrate that the proposed VLC-NOMA scheme outperforms than state-of-the-art orthogonal frequency division multiple access(OFDMA) one in terms of SER performance.Finally,relationships between the SER performance and the number of users,power allocation coefficient and semi-angle are well investigated,which can give us a scientific guide to devise the VLC-NOMA system for achieving better SER performance.

Non-Contact Method of Heart Rate Measurement Based on Facial Tracking

Image photoplethysmography can realize low-cost and easy-to-operate non-contact heart rate detection from the facial video, and effectively overcome the limitations of traditional contact method in daily vital sign monitoring. However, it is hard to obtain more accurate heart rate detection values under the conditions of subject’s facial movement, weak ambient light intensity and long detection distance, etc. In this article, a non-contact heart rate detection method based on face tracking is proposed, which can effectively improve the accuracy of non-contact heart rate detection method in practical application. The corner tracker algorithm is used to track the human face to reduce the motion artifact caused by the movement of the subject’s face and enhance the use value of the signal. And the maximum ratio combining algorithm is used to weight the pixel space pulse wave signal in the facial region of interest to improve the pulse wave extraction accuracy. We analyzed the facial images collected under different experimental distances and action states. This proposed method significantly reduces the error rate compared with the independent component analysis method. After theoretical analysis and experimental verification, this method effectively reduces the error rate under different experimental variables and has good consistency with the heart rate value collected by the medical physiological vest. This method will help to improve the accuracy of non-contact heart rate detection in complex environments.

Self-determinate evaluation method based on condition of weights non-dictatorial rate

The condition of weightes non-dictatorship is extended and a comprehensive evaluae method emboding self-determinate which is combined with competitive view optimization principles is built. The basic process includes simulating the model of economic man＇s self-benefit bahaviors, taking the place of experts to evaluate, bringing in the model of minimizing the sum of included angles to integrate the information of multiple objects and put the objects in order finally. The method has the advangtages of less dependendence on the subjective information, plenty of information, fair process and simple caculating. Finally, an application example is given to illustrate the effectiveness of the proposed method.

Estimation of Critical Rate of Temperature Rise for Thermal Explosion of First Order Autocatalytic Decomposition Reaction Systems by Using Non-isothermal DSC

A method of estimating the critical rate of temperature rise for the thermal explosion of first order autocatalytic decomposition reaction systems by using non-isothermal DSC is presented. The information was obtained on the increasing rate of temperature for the first order autocatalytic decomposition of nitrocellulose containing 13.86% nitrogen converting into the thermal explosion.

Fixed Dose Rate versus Standard Dose Rate Infusion of Gemcitabine and Cisplatin in Advanced Stage Non-Small Cell Lung Cancer

Background: Comparing the efficacy and safety of gemcitabine at a fixed-dose rate (FDR) infusion (10 mg/m2/min) with the standard dose rate infusion in patients with locally advanced and metastatic non-small squamous cell carcinoma (NSCLC). Methods: The study randomized 60 patients with confirmed diagnosis of NSCLC to receive gemcitabine at a dose of 1000 mg/m2 on days 1 and 8 given as a 30-min infusion (Arm A) or at a rate of 10 mg/m2/min (Arm B). Cisplatin 75 mg/m2 was administered intravenously on day 2 in both arms. Results: No difference in overall response rate (46.6% versus 43.3%). Median time to progression for Arm A was 7 months (95% CI, 6.207 - 7.793 months), versus 6 months for Arm B (95% CI, 4.990 - 7.010 months). Median survival time was comparable [12 months (95% CI, 8.588 - 15.412 months) versus 11 months (95% CI, 9.066 - 12.934 months)] respectively. Two-year survival (18% versus 11%, p = 0.38) was detected. No treatment related deaths occurred. Main hematological toxicities were grade I and II neutropenia, in 36.7% and 53.3% respectively (p = 0.044). Grade III anemia was observed in 10% and 6.7% in both arms respectively (p = 0.024). Grade I and II nausea and vomiting was observed in 50% and 46.7%. Conclusions: FDR gemcitabine in combination with cisplatin had equivalent efficacy and more severe hematologic toxicities compared to the standard 30-min gemcitabine infusion with cisplatin in patients with advanced NSCLC.

Low-temperature performance and high-rate discharge capability of AB_5-type non-stoichiometric hydrogen storage alloy

Low-temperature performance and high-rate discharge capability of AB5-type non-stoichiometric hydrogen storage are studied. X-ray diffraction(XRD),pressure-composition-temperature(PCT) curves and electrochemical impedance spectroscopy(EIS) are applied to characterize the electrochemical properties of ABx(x=4.8,4.9,5.0,5.1,5.2) alloys. The results show that the non-stoichiometric alloys exhibit better electrochemical properties compared with that of the AB5 alloy.

Exploiting Virtual Elasticity of Manufacturing Systems to Respect OTD—Part 2: Post-Optimality Conditions for the Cases of Ergodic and Non-Ergodic Order Rate with Deterministic Product-Mix

Respecting the on-time delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed. As an OTD related manufacturing theory is largely missing it is crucial to understand and formalize the necessary conditions of OTD compliance for complex production environments for maximum exploitation of the production capacity. This paper evaluates the conditions of post-optimality while being OTD compliant for production systems, which are characterized by stochastic order rate and a deterministic product-mix. Instead of applying discrete event simulation to explore the real case-by-case order scheduling optimization for OTD compliance, a Cartesian approach is followed. This enables to define theoretically the solution space of order backlog for OTD, which contributes to developing further manufacturing theory. At the base stands the recently defined new concept of virtual manufacturing elasticity by reducing lead-time to increase virtually production capacity. The result has led to defining additional two corollaries to the OTD theorem, which sets up basic OTD theory. Apart from defining the post-optimal requirements to guarantee for orders at least a weak solution for OTD compliance, this paper reveals that for a deterministic product-mix a non-ergodic order arrival rate can be rescheduled into an ergodic order input rate to the shopfloor if the virtual elasticity T is large enough, hence the importance of having fast and flexible production lines.

STANCU POLYNOMIALS BASED ON THE Q-INTEGERS

A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.

Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates

The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.

Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations

In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper.

Performance Analysis of Outage Probability and Error Rate of Square M-QAM in Mobile Wireless Communication Systems over Generalized α-μ Fading Channels with Non-Gaussian Noise

This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.

Distribution Pattern of the Non Polio Enterovirus (NPEV) Rate in Children with Acute Flaccid Paralysis Reported to the Surveillance System in Nigeria 2010-2015

Objective: This study focuses on the reverse cold chain system of stool sample management from cases reported to the AFP surveillance system between 2010 and 2015. Through the distribution of their NPEV isolation rates, we identify lapses in the reverse cold chain management and provide recommendations that should help improve the reverse cold chain system and the AFP surveillance system in general as Nigeria once again matches towards a polio free certification. Methods: A descriptive retrospective study was conducted using AFP surveillance data routinely collected between January 2010 and December 2015 by the Disease Surveillance and Notification Officers (DSNOs) in Nigeria and the WHO accredited Polio Laboratories. All AFP cases reported to the Disease Surveillance network during this period from all the states were included in the study. EPIINFO—veritable customized software was used to run queries on the access database and obtain the specific data sets required. Results: A total of 52,879 AFP cases were reported from 2010-2015, in which 7288 non-polio enteroviruses were isolated. NPEV isolation rate ranged from 10.8% in the southeast to 20.3% in the northeast with the states in the northern geopolitical zones having higher NPEV rates in comparison to the states in the southern geopolitical zones. The WHO Polio laboratory in Ibadan serves twenty-seven states in the country;the average non-polio AFP rate among states served by this laboratory is 11.7% from a total of 4012 AFP cases recorded. The WHO Polio laboratory in Maiduguri recorded 3276 with an average non-polio AFP rate of 19.2%. Conclusion: Though the country’s NPEV isolation rate remain slightly higher above the 10% recommended by WHO, steps should be taken to enhance the reverse cold-chain system particularly in the southern states. This would increase confidence in the AFP surveillance system in Nigeria as she proceeds once again towards complete polio eradication and meeting certification standards.

Forecasting of Survival Rate in Patients with the Early Stage of Non Small Cell Lung Cancer

Lung cancer is the most common cause of death from oncological diseases all over the world. Primary treatment of patients with the early stage of non-small cell lung cancer is a surgery. However, after surgery 30% - 85% of patients undergo disease progression. In order to improve the results of treatment of patients with non-small cell lung cancer it is necessary to separate a group of patients with dismal prognosis for whom adjuvant chemotherapy will permit improving the survival rate. The aim of our research was to create a forecasting model with a view to detect the patients with the early stage of non-small cell lung cancer and dismal prognosis. Our research covered 254 patients with the early stage of non-small cell lung cancer who underwent a cure from June 2008 till December 2012 in the department of thoracic surgery of Zaporizhzhia Regional Clinical Oncologic Dispensary. In order to identify the factors connected with the risks of low survival rate of patients with the early stage of non-small cell lung cancer after curative treatment (surgical treatment, adjuvant chemotherapy), a method of design of neural network models of classification was used. 39 factors were taken for input characteristics. During investigation two forecasting models were built. As follows from the analysis of first forecasting model with the increase of the patient’s BMI, the risk of low patient survival rate statistically and significantly (p = 0.03) decreases, OR = 0.89 (95% CI 0.80 - 0.99) for each kg/m2 index value. The risk of low patient survival rate also decreases (p = 0.02) if he has a squamous cell carcinoma, OR = 0.36 (95% CI 0.15 - 0.88) compared with other histological forms of tumor. The connection between the risk of low patient survival rate and the volume of surgical intervention was discovered (p = 0.01), OR = 3.19 (95% CI 1.29 - 7.86) for patients who underwent a pulmonectomy compared with patients who underwent an upper bilobectomy. As follows from the analysis of second forecasting model with the increase of the patient’s BMI the risk of low patient survival rate statistically and significantly (p = 0.01) decreases;OR = 0.84 (95% CI 0.74 - 0.96) for each kg/m2 index value. It is found that with the increasing level of EGFR expression in the primary tumor, the risk of low patient survival rate statistically and significantly increases (p = 0.04), OR = 1.39 (95% CI 1.01 - 1.90) for each graduation rate. The risk of low patient survival rate also increases when conducting the lymph dissection in the volume D0 - D1.

Usage of Cox-Regression Model for Forecasting of Survival Rate in Patients with the Early Stage of Non-Small Cell Lung Cancer

In the past decades a lot of investigations were focused on searching for more accurate markers of lung cancer progression. Researchers indicate that molecular markers may be useful in forecasting of treatment outcome and overall survival rate in patients with non-small cell lung cancer. The aim of our research was to create a forecasting model in order to identify patients with stage I-II of non-small cell lung cancer and dismal prognosis. Our research covered 254 patients with the early stage of non-small cell lung cancer who underwent a cure from June 2008 till December2012 inthe Department of Thoracic Surgery of Zaporizhzhia Regional Clinical Oncologic Dispensary. Surgery was performed for all patients. Adjuvant chemotherapy was performed for 101 patients. In order to carry out multivariate Cox-regression analysis, STATISTICA 6.0 (StatSoft Inc.) program was used. The most significant from 39 variables were selected (tumor size, histological form of tumor, volume of surgical intervention, volume of conducted lymph node dissection, Ki-67 expression, EGFR expression, E-cadherin expression). We propose the computer system which can forecast survival rate in patients with the early stage of non-small cell lung cancer.

Non-invasive foetal heartbeat rate extraction from an underdetermined single signal

Extraction of foetal heartbeat rate from a single passive sound sensor on the mother’s abdomen is demonstrated. The extraction is based on the assumption that a disjoint band of frequencies exist and foetal signal is concentrated in this band, and further that it can be represented conveniently as a set of wavelet coefficients. The algorithm has been applied to each stream of data obtained from six different channels and the detection performance is elaborated. The algorithm has also been tested on signals from non-pregnant abdomens to show successful rejection of adult heartbeat. The extraction of the desired signal is done in two stages so as to eliminate components from the maternal heart-beat.

Very Low, Real-Time Rate of Urinary Retention after Intradetrusor Botox^&regfor Non-Neurogenic Overactive Bladder

Introduction: According to the most recent AUA/SUFU guidelines, intradetrusor onabotulinumtoxinA (BTN/A) is a standard, evidence strength grade B, third line treatment option for refractory non-neurogenic overactive bladder (OAB). Urinary retention is the most common clinically significant reported side effect ranging from 5.4% to 43% in previous studies. The aim of this study was to investigate the real-time rate of urinary retention in patients treated with BTN/A for refractory non-neurogenic OAB in a multi-institutional study. Methods: Retrospective chart review identified 71 patients who were treated with 100U BTN/A for refractory non-neurogenic OAB from August 2011 to July 2015 at two institutions. Using a flexible cystoscope, 100U Botox&reg reconstituted with 10 ml normal saline was administered. Injections of 1 ml (10 units/ mL) were administered in 10 evenly distributed sites sparing the trigone. Pre and post BTN/A post-void residuals (PVR) were reviewed. Urinary retention was defined as PVR > 200 mL requiring clean intermittent catheterization (CIC). Results: After exclusion, the study group consisted of 66 patients with a mean age of 67 years and 30% were men. Mean pre and post-procedural PVR were 14.06 mL and 69.21 mL. Eight patients (12.12%) were noted to have elevated PVR > 200 mL post injection however only one patient (female) required initiation of CIC. The rate of urinary retention was 1.5% (N = 1). There was no correlation with age, history of previous radiation, diabetes or prior use of a neuromodulator device. Conclusions: To the best of our knowledge, this is the first study to demonstrate a very low risk of real-time urinary retention rates in appropriately selected patients treated with BTN/A for refractory non-neurogenic OAB outside of a clinical trial setting.