Geometric Progression Research Articles

Uncompensated Centrifugal Flow about Accelerated Cosmic Expansion

Currently, we are under the perception of a visible universe which has an accelerated expansion, because repeated evidences obtained by several technics since the well known observations performed by Edwin Powell Hubble. The world scientific community was astonished by these observations, and since then until today, countless calculations have been made that only leave the hypothesis of the existence of an unknown cosmic entity that has the particularity of repelling matter from each other when it is sufficiently separated by huge amounts of that entity, which was called as “dark energy”. This “dark energy” is a completely unknown thing, and it is understood by some researchers as the convenient hypothesis, because it is which emerges from deep calculations and observations. Bearing in mind that we already know about all cosmic objects and systems are in rotation, both locally and not so locally, and that everything is full and endowed with intrinsic and extrinsic angular momentum, it seems logical to think that rotational dynamics must also apply to the more extensive, and that if locally (and not so locally) we perceive and infer rotating objects everywhere, then they must also exist globally. So, starting from the idea that rotation is omnipresent, at every level of sizes; from the invisibly small to the invisibly large, I thought that it is really wise to cover it through rotation dynamics, or that in the worst case, we cannot ignore the fact of the omnipresent rotation in any entity to infer. And this is the main reason for the resolution and the motivation of the birth of the publication of this study. Based on this seemingly simple idea, these results and conclusions of this study was reached: following a formal logic and evidence of the accelerated unfolding of the cosmic fabric, another hypothesis is proposed as an alternative to the existence of the “dark energy”: The intensities of centrifugal acceleration fluxes exceed the intensities of gravitational fluxes, which are not sufficient to compensate for the centrifugal flux, which is why baryonic and exotic matter, energy, space and time are extended, in geometric progression with respect to our apparent time. So, this unfolding of the cosmic fabric might not be caused by a “dark energy”, but by centrifugal fields of rotational-orbital domains. Besides all the above, this publication has a double purpose, because it is also intended to cover another matter; these deep attentions to the Rotational Dynamics also derive in another solution or hypothesis regarding the formed mystery after observing the incoherent too high velocity of matter in the far latitudes in spiral galaxies: The hypothesis of the existence of the so-called “dark matter” arises from the observation that, in spiral galaxies, all that matter which is located beyond a critical distance from the galactic rotation axis, travels too fast, while the calculations illustrate an insufficient intensity of gravitational acceleration flux to explain that speed and to retain all that matter while maintaining the orbital distance. However, the concept I present here, is that, in a spiral galaxy, all those matter which is positioned farthest from the main rotation axis, is effectively lost in space as time goes by, or what is the same, the intensity of the centrifugal acceleration field is not compensated by that of the gravitational field, and the destiny of every spiral galaxy is a more or less homogeneous and compact disk-shaped galaxy. As a basic NOTE to be taken into account; in the present article we intend to show the radical, meticulous and delicate relation that exists in the considerations of the classic concept of “isolated system of particles”, with the degrees of the consistencies of the connections between all those “particles”, whether they are inter-material bonds, or, in a relativistic scope, bonds between the same cosmic fabric. And this is so, because the idea of “isolated” falls directly and precisely on the criterion that we put to the degree of consistency of each connection between each “part” or “particle” that integrates the presumed and inferred concept of “isolated system” with respect to the rest of systems or universe.

Analgesic and anti-inflammatory activity of Artemisia extracts on animal models of nociception

Introduction. The study aims to assess the antinociceptive and anti-inflammatory activity of extracts obtained from indigenous species of wormwood: Artemisia absinthium, A. annua, A. vulgaris and A. pontica. Materials and methods. For these experiments, we employed nociception models using thermal stimulus (hot plate and tail immersion tests, t = 52.5 0C; 30, 60 and 90 minutes testing), chemical stimulus (Zymosan-induced abdominal constriction response test, using distinct lots and testing at 60, 90 and 120 minutes after administration of samples) and pressure stimulus (Randall Selitto test) and an inflammation model for the evaluation of inflammatory edema by Plethysmometer test. Groups of 6 Swiss mice / lot were used, receiving by oral administration the plant extracts suspended in 0.1% CMC-Na. The doses were administered in geometric progression. Chemical analyses were performed by HPLC-MS in order to identify bioactive substances present in extracts: methoxylated flavonoids, sesquiterpene lactones, phytosterols and hydroxycinnamic acids. Results and discussion. All plant extracts showed antinociceptive action on the models with thermal stimulus, as demonstrated by the ED50 values obtained at different test times. In the models of nociception with chemical and mechanical stimulus, models based on inflammatory mediation, the studied fractions have partially proved their antinociceptive action. Regarding the degree of inhibition of inflammatory edema, the highest potency was exhibited by Artemisia pontica extract (86.5% inhibition for the dose of 100 mg/kg). Hispidulin and eupatorin, known anti-inflammatory compounds, were identified in all extracts, along with caffeic and chlorogenic acids, stigmasterol, campesterol and β-sitosterol. Conclusions. The obtained results support the use of these plant extracts in moderate intensity pain, triggered by both central and peripheral mechanisms. Keywords: hot-plate test, tail immersion test, abdominal constrictive response, Randall-Selitto test, inflammatory edema,

An Alternative to Dark Matter? Part 1: The Early Universe (<i>t<sub>p</sub></i> to 10<sup>-9</sup> s), Energy Creation the Alphaton, Baryogenesis

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe U, cosmological constant Λ, the curvature of space k, energy density ρΛe, age of the universe tΩ etc. The development of the state equation highlights the importance of not neglecting any of the differential terms given the very large amounts in play that can counterbalance the infinitesimals. Some assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, tp, the universe contained a single photon at Planck temperature TP, almost Planck energy EP in the Planck volume. During the photon inflation phase (before characteristic time ~10-9 [s]), the number of original photons (alphatons) increased at each unit of Planck time tp and geometrical progression~n3, where n is the quotient of cosmic time over Planck time t/tp. Then, the primordial number of photons reached a maximum of N~1089, where it remained constant. These primordial photons (alphatons) are still present today and represent the essential of the energy contained in the universe via the cosmological constant expressed in the form of energy EΛ. Such geometric growth in the number of photons can bring a solution to the horizon problem through γγ exchange and a photon energy volume that is in phase with that of the volume energy of the universe. The predicted total mass (p, n, e, and ν), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 1050 [kg]. The predicted cosmic neutrino mass is ≤8.69 × 10-32 [kg] (≤48.7 [keV·c-2]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (ΔU/U) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons).

Switched Capacitor Bank Design With Geometric Progression for Wideband Frequency Doubler

Switched Capacitor Bank Design With Geometric Progression for Wideband Frequency Doubler

Exposure buildup factor investigation of tungsten gadoliniumborate system

Abstract The gamma ray exposure buildup factors (EBF) of xWO3:(70-x)Gd2O3:30B2O3 system (where x=40, 45, 50, 55 and 60 mol%) have been calculated in the energy region 0.015–15 MeV up to a penetration depth of 40 mfp (mean free path). The five parameter geometric progressions (G-P) fitting method has been used to compute exposure buildup factor values. Variation of exposure buildup factors with incident photon energies and penetration depth have been studied. It was found that EBF values were higher in the intermediate energy region, for all glass system. Moreover, tungsten gadolinium borate glass of 40 mol% WO3, was found to present the lowest EBF values, hence it is excellent gamma ray shielding material. The obtained results in this paper show that these glasses can be used as radiation shielding materials

Economic viability of foreign investment in public transport of Pakistan – orange line metro train in focus

Pakistan, like other developing countries, is also facing environmental and economic challenges in its transportation sector (especially in public transport). Pakistan is going to get finances for the infrastructure-related projects under the China-Pakistan Economic Corridor (CPEC) initiative. One of the CPEC projects is the Orange Line Metro Train (OLMT). The study employs traditional techniques such as linear trend regression, benefit-cost ratio (BCR) and geometric progression to analyse the economic viability of the project. The results show that with given interest rate and stability in exchange rate the project is economically viable, with a benefit/cost ratio (BCR) of 2.11 and Internal Rate of Return (IRR) equal to 3.07 per cent. Furthermore, the sensitivity analysis is done for possible changes in economic conditions as well as for different interest rates for loan repayments. The study is useful for policymakers interested in the benefit–cost analysis of public transportation projects.

Ontogeny and Anatomy of the Dimorphic Pitchers of Nepenthes rafflesiana Jack.

An enigmatic feature of tropical pitcher plants belonging to the genus Nepenthes is their dimorphic prey-capturing pitfall traps. In many species, the conspicuously shaped upper and lower pitchers grow from a swollen leaf tendril tip until finally opening as insect-alluring devices. Few have studied the ontogeny of these traps from an anatomical and quantitative morphological perspective. We investigated whether the anatomy and development of lower and upper type pitchers of N. rafflesiana differ or overlap in terms of 3D geometric morphology and microstructure progression and presence. We hypothesized that there is an overlap in the initial, but not all, developmental stages of the two pitcher types and that one pitcher type is suspended in development. We identified four important morphological changes of pitcher ontogeny and defined these as curvation, elongation, inflation and maturation phases. Pitcher length indicated progress through developmental phases, and we propose to use it as a tool for indication of developmental stage. Microstructure development coincided with the developmental phases defined. Additionally, we discovered a new anatomical feature of extrafloral nectariferous peristomal glands between the inner peristome ridges of upper and lower pitchers being hollow and analyze the chemistry of the sugars on the outside of these glands. Ontogenetic shape analysis indicated that upper and lower pitcher types develop with similar phase progression but have no directly overlapping morphology. This means that upper pitchers are not a derived state from lower pitchers. Independent developmental programs evolved to produce distinctly shaped upper and lower pitchers in Nepenthes, likely to exploit different food sources.

Epidemiological Assessment and Challenges of the COVID-19 Pandemic in Nigeria

The COVID-19 which belongs to the coronaviridae family has continued to spread in a geometric progression version. The disease that originated from Wuhan, Hubei, China has spread to all the continents of the World except Antarctica continent. As of the 5th of August, 2020 there are over 18 million reported cases of COVID-19 from 214 countries and territories of the world. More than 10 million people have recovered while approximately 696,147 people have died due to COVID-19. This review provides general information on the COVID-19 and gives deep insight into the course of the disease, interventions challenges and possible solutions in Nigeria “the giant of Africa”.
 Scientific databases including Science Direct, Pub Med, Elsevier, Scopus, and Nature were explored. Data has also been accessed from case reports, newspaper reports, internet data, World Health Organisation (WHO) reports, Centre of Disease Control (CDCs) and Nigerian Centre of Disease Control (NCDCs) reports. US National Library of Medicine, Clinicaltrials.gov, has been accessed to get information about ongoing clinical trials. The literature survey started in the first week of April, 2020 and was completed in the first week of August, 2020. The clinical symptoms of COVID-19 patients are generally categorized as critical, severe, moderate and mild or even asymptomatic in descending order in terms of severity. Predictions from experts in different parts of the World concerning the possible impact of the disease in Africa have been on the downside which is due to a lot of glaring factors including poor health facilities and services.

EFFECTS OF URBAN EXPANSION ON VEGETATION COVER LOSS IN LAGOS STATE, NIGERIA

Urbanization is a significant human activity affecting the environment. The study analyzes land use/land cover changes and examines built-up expansion through multi-temporal Landsat images spanning 1985 to 2015. In order to assess the pattern of urbanization, land consumption ratio (LCR) and land absorption coefficient (LAC) have been estimated. In 1985, vegetation cover occupied 54.70%, water bodies accounted for 22.10%, and built-up/open area accounted for 15.80% of the total study area. However, in 2015, vegetation and water bodies reduced drastically to 42.60% and 17.90% while there was a geometric progression in built-up/open area accounting for 39.50% of the entire study area. Also, between 1985-2015, vegetation cover and water bodies declined by 0.74% and 0.63% while the built-up/open area increased at an average rate of 4.99% per annum. The analysis of land consumption ratio revealed that built-up expansion has led to a high level of consumption of vegetation cover and water bodies at the rate of 0.016, 0.007 and 0.006 in 1985, 2000 and 2015 respectively. Similarly, land absorption coefficient accounted for 0.002 and 0.005 between the periods of 1985-2000 and 2000-2015. The rate of land acquisition indicates that development is high over the 30 years leading to a decline of green areas. If the present trend continues, it will lead to severe degradation of urban micro-biome, especially wetland resources, hence the call for a proper land-use policy for Lagos and other similar megacities in Nigeria.

Nb2O5-Li2O-Bi2O3-B2O3 novel glassy system: evaluation of optical, mechanical, and gamma shielding parameters

For the Nb2O5-Li2O-Bi2O3-B2O3 glass system, optical, structure, mechanical gamma, and neutron radiation shielding aspects were examined comprehensively. The two probabilities of the bandgaps, direct and indirect transition, were evaluated. The absorbance of the recent glasses was increased as Nb2O5 increased. Moreover, the peak shifted to a longer wavelength as Nb2O5 increased. Our results show a decreasing behavior of both kinds of the bandgap. Adopting XCOM within 0.04–15 MeV, LAC and MAC were evaluated for all samples and calculated MAC values are in excellent compliance with deduced FLUKA code respective MAC outcomes. Zeff, HVL, and MFP values were estimated. MAC, Zeff, HVL, and MFP values depended on glass components and energy. Moreover, using equivalent atomic numbers (Zeq) and the geometric progression fitting procedure, EABF values were calculated up to 40 mfp, within 0.015–15 MeV. Comparatively higher density (4.9454 g/cm3), greater LAC, MAC, Zeff, Zeq, and lower HVL, MFP, EABF values achieved for 10Nb2O5-10Li2O-30Bi2O3-50B2O3 glass indicated it as a better gamma shield. Furthermore, the calculated ΣR shows that the 10Nb2O5-10Li2O-30Bi2O3-50B2O3 sample has commensurately greater ΣR (= 0.1744 cm−1).

Global Challenges on Environmental Sustainability: A Reflection on Policies and Applications

The study evaluates global environmental sustainability challenges placing emphasis on policy formulation and commitment to policy implementation among stakeholders. It is imperative for public assessment and reporting of progress and commitment towards environmental sustainability. It is believed that measuring progress on sustainable development with reliable information is a key ingredient of the democratic process. It makes governments more accountable and gives people a tool to participate more actively in defining and assessing policy goals. The study using mainly secondary sources and content analysis concludes that, not much seems to have been done; the world leadership is still not ready to live up to expectation given the constant, consistent degeneration and destruction of our planet earth in geometric progression. It has become a collective responsibility for all entities to purposefully strive using all means to attract requisite attention that would compel responsible authorities to live up to expectation.

LYSOSOMOTROPIC PROPERTIES OF SODIUM BICARBONATE AND COVID-19

SARS-CoV-2 causing COVID-19 has appeared as an ongoing global public crisis, growing with geometric progression and has caused huge devastation till date majorly because of lack of targeted therapeutic agents like vaccines. SARS-Cov-2 entrance into the host cells is reliant on acidic pH. Thus, in the current clinical emergency there is a pressing need to look forward for adjunct therapies which could counter the acidic pH, so as to restrain the viral entry and its subsequent reproduction in the host cells. Therefore, the current review attempted to explore the possibility to use sodium bicarbonate as an alternative lysosomotropic agent based on the reported literature owing to its anti-flu properties and widespread use during 1918 Spanish flu pandemic. The suggestions put forward in the current review article based on the careful use of sodium bicarbonate could probably help to restrain SARS-CoV-2 infection.

Binary B2O3–Bi2O3 glasses: scrutinization of directly and indirectly ionizing radiations shielding abilities

For five B2O3–Bi2O3 glasses, detailedly, γ, neutron, & proton, alpha, and electron (charged particles) shielding efficacies were assessed in this work. The crucial photon attenuating (interaction probabilities) parameter i.e., mass attenuation coefficient (μ/ρ) was calculated by Phy-X/PSD software and procured μ/ρ results have been verified through MCNPX, Geant4, & FLUKA codes μ/ρ findings from which a quality unanimity among them was noticed over an energy range of 15 KeV–15 MeV. Following μ/ρ & linear attenuation coefficient (μ) outcomes, Zeff, Neff, HVL, TVL, and MFP have been reckoned and found that all μ/ρ, Zeff, Neff, HVL, TVL, & MFP highly rest on glass chemical contents & photon energy. Zeq and by applying geometric progression (G‒P) fitting parameters (a, b, c, d, & Xk coefficients) EBFs & EABFs were appraised at ten specific penetration depths up to 40 mfp, at energy range of 0.015–15 MeV. The inferred RPE quantities confirmed all chosen glasses quintessential absorption competence for lower energy γ-rays. Utilizing SRIM code the mass stopping powers (MSPs) & projected ranges (PRs) for protons ((ΨP)&(ΦP)) and alpha particles (ΨA)&(ΦA), and with the help of ESTAR database, electron MSP (ΨE) & continuous slowing down approximation (CSDA) ranges for electrons have been approximated at 0.015–15 MeV KE. The fast neutron removal cross-sections (ΣR) were estimated and obtained ΣR was diversified at 0.10978–0.12144 cm−1 range relying on Bi2O3 inclusion in glasses. Based on all acquired outputs, 57.5B2O3-42.5Bi2O3 (mol%) glass possesses superior attenuation capacity for γ-rays and fast neutrons as well as charged particles.

Algorithm for compensation of walking disturbances of a two-legged robot by solving the inverse problem of kinematics

Actual problem of design of biped robot walking is presented. New algorithm for determination of motion laws of low limbs links of biped robot at walking is presented for given walking characteristics such as lengths and height of step, velocity, foot sizes, kinematic model of limbs, inertial characteristics of all links. The position of the reference polygon while walking is designed at first. By means of this data the law of ZMP motion is defined by approximation by means of straight lines and parabolas of the 5th order. To increase the accuracy of decomposition of non periodic functions in Fourier series the linear trend is removed from it. Comparison of left hand and right hand harmonics of differential equation connecting coordinates ZMP and COM forms motion law of robot’s mass center. This, along with the well-known law of motion of the feet when walking, allows one to find the laws of motion of all the links involved in walking. Existing nonlinear equations are solved by Newton's method. The performance of the algorithm is assessed by using it in the framework of another algorithm that calculates compensatory effects during walking to maintain dynamic balance. Compensation of the arising disturbances is carried out by distributing them in half or in a whole step using a geometric or arithmetic progression. The accuracy and the achieved performance for the implementation of these algorithms in the on-board computer of the robot are registered.

Bouncing Balls and Geometric Progressions

Observing the bouncing of a marble on a table is a rather common experience. The tic-tac sound of the rigid ball, nevertheless, carries quite a pleasant surprise. In fact, by measuring the total time of bouncing Δt, the coefficient of restitution can be estimated. As is well known, in an inelastic collision the kinetic energy is not conserved, and therefore the speed decreases. The speeds vi and vf, before and after the collision occurs, respectively, are related as follows: νf=ενi,(1) where ε < 1. By measuring the initial height h0 from which the marble is released, we find that ε=T−2h0gT+2h0g,(2) where g is the acceleration due to gravity and T is the total time from initial release until the ball stops bouncing.

Per‐stage growth rates of head and body sizes in scarab larvae (Coleoptera: Scarabaeidae) decrease across ontogeny following a species‐specific pattern

AbstractIt has been widely assumed that the stepwise increase in the exoskeleton size of larval insects approximately follows a geometric progression from instar to instar, known as Dyar's Rule. However, it is not clear whether the per‐instar increase in body size follows this rule. In insects, Dyar's Rule has been identified either by regressing the log‐scaled size on the instar number (log‐linear regression analysis) or by comparing the postmolt/premolt size ratio between instars (growth rate analysis). A previous study on the body mass of caterpillars showed the methodological pitfall that Dyar's Rule was statistically supported by log‐linear regression analysis, but not at all by growth rates analysis. I considered this concern here by examining the per‐stage growth rates of head and body sizes for larvae of the beetle Trypoxylus dichotomus using both methods and compared the resulting growth rates for body size within and between taxonomic orders. Dyar's Rule was statistically supported by the log‐linear regression analysis but not by growth rate analysis for both the head and body sizes in T. dichotomus. The body size growth rate in T. dichotomus decreased as the instar progressed. This developmental pattern was also found in reported data for the other six scarabs, but not in data for Lepidoptera or Hymenoptera. These findings confirm that the per‐stage growth rate of body size does not follow Dyar's Rule in a wide range of insects, and suggest that developmental change in the body size growth rate varies among insect groups.

Geometric progressions in vector sumsets over finite fields

Given two subsets A,B of the d dimensional vector space over the finite field Fq of q elements, we show that the sumsetA+B={a+b|a∈A,b∈B} contains k distinct vectors of the form (v1λ1j,…,vdλdj), where j=0,…,k−1, with nonzero vectors (v1,…,vd),(λ1,…,λd)∈Fqd, whenever#A#B⩾cq2d(1−1/k), for some constant c>0 which depends only on k. This improves the previous result of O. Ahamadi and I.E. Shparlinski (2007), which has the exponent 2d−2/k.

Forecasting of COVID-19 Cases in Kurdistan Region Using Some Statistical Models

Nowadays the new universal disease of the coronavirus that is called the epidemic COVID-19 is spread as geometric progression among the people around the world, so, such pathogen considered the most dangerous threat facing humanity. This study aimed to derive the best forecasting models for the close future cases of infected, recovered, and deaths in the four provinces of Kurdistan Region-Iraq to avoid more loss of human lives by applying more health care in certain province. Two forecasting methods were used including Exponential Smoothing and ARIMA models. The results indicate that both ARIMA and Exponential Smoothing models were close to each other for predicting the infected cases of COVID-19 in Kurdistan Region provinces, and the predicting models show that the pandemic might not be under control unless the people apply the government instructions for health care and keep social distances.

Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

AbstractIn this article, we propose to investigate numerically the steady bifurcation points and bifurcated branches in fluid mechanics by employing high‐order mesh‐free geometric progression algorithms. These algorithms are based on the use of the geometric progression (GP) in a high‐order mesh‐free approach. The first proposed algorithm is applied on a strong formulation using the moving least squares (MLS) approximation coupled with GP (HO‐MLS‐GPM). While the second proposed algorithm is applied on a weak formulation using the element‐free Galerkin (EFG) coupled also with GP (HO‐EFG‐GPM). The incompressibility condition is taken by introducing the penalty technique to transform the stationary Navier–Stokes equations verified by the pressure and velocity into ones verified by only the velocity. The high‐order mesh‐free algorithm permits to transform this nonlinear equations into a succession of linear ones. The GP allows to detect with precision the bifurcation points and the Lyapunov–Schmidt reduction is coupled with HO‐MLS‐GPM and HO‐EFG‐GPM as a continuation procedure to follow the many bifurcated branches. The aim of this resolution strategy concerns the treatment of the bifurcation phenomena for a fluid flow through an expansion in several geometries, where the steady flow becomes unstable after a critical Reynolds value. The obtained results are compared with those presented in literature and with those computed using the high‐order finite element algorithm coupled with GP.

Buildup with Bremsstrahlung in the Martian Atmosphere

Photon buildup is a function of energy, medium, and geometry and therefore must be specifically calculated for the case of interest. The Martian atmosphere, mostly comprising carbon dioxide, is becoming more relevant to radiation researchers and therefore warrants the study of this gas mixture’s buildup properties for ionizing photon flux resulting from the secondary effects of galactic cosmic rays and solar flares. Specifically, this work uses the MCNP6 code to develop energy absorption buildup factors in finite slab models for energies ranging from 40 keV to 15 MeV with Martian regolith as the backscattering medium. The Martian carbon dioxide cycle is accounted for by determining maximum and minimum mean densities as a function of orbital position. An isotropic point source model for the atmosphere is also developed using the geometric progression fitting function. Buildup is bounded to a factor of approximately 23 at 100 keV for normally incident photons at the top of the atmosphere. For conservatism, the design problem neglects coherent scattering but assumes bremsstrahlung effects and uses Klein-Nishina free-electron cross sections for Compton scattering.