Complete Equilibrium Research Articles

YOGA AND HOLISTIC HEALTH

Yoga is an ancient art based on a harmonizing system of complete equilibrium of body, mind, and spirit. The link to yoga is asana. Holistic health is an approach to life, rather than focusing on illness or a specific part of the body. The holistic health approach considers the whole person and how he or she interacts with his or her environment. It emphasizes physical, mental, social, spiritual, and, intellectual. Yoga means union, so yoga is the union of the mind emotions, and the body. Holistic wellness is significant between physical health and mental health. Yoga is a holistic science, it seeks to build a lifestyle that values calmness, harmony, and positive thinking. Multiple-way yoga approach helps towards the health and well-being of humans. India ‘s invaluable gift is yoga. Many research finding concludes yoga play in holistic care.

Sorption of silver (I) ions from aqueous solutions using the synthetic sorbent

We study the sorption of silver ions from aqueous solutions by a synthetic chelating sorbent. In the presence of formaldehyde, a polymeric sorbent based on a copolymer of styrene with maleic anhydride, modified with N,N’-diphenylguanidine, was synthesized and further used for extracting Ag(I) ions. The composition and structure of the synthesized polymeric chelating sorbent were studied using IR and UV spectroscopy methods. A simple, inexpensive, and efficient method for extracting Ag(I) ions from aqueous solutions was used. The effect of various parameters on the sorption process was studied, including the acidity of the medium (pH), the initial concentration of the metal ion, the time required to establish complete sorption equilibrium, and ionic strength. The optimum pH value for the extraction of Ag(I) was found to be 6. The process is characterized by a high adsorption capacity reaching 547.2 mg/g. The research results showed that the time required to establish a complete sorption equilibrium for the sorbent modified with N,N’- diphenylguanidine is 60 min. Ag(I) adsorption increases up to the value of ionic strength of μ = 1, after which its intensity decreases. At the final stage, the process of desorption of absorbed silver ions was carried out. During desorption, the best eluting agent for the extraction of Ag(I) was determined to be 0.5 M HNO3. The sorbent can be re-used after regeneration. The copolymer of styrene and maleic anhydride modified with N,N’-diphenylguanidine has a high sorption capacity and, therefore, can be used as a potential adsorbent for the extraction of silver (I) from aqueous solutions.

Nitrogen-rich carbon nitrogen polymers for enhancing the sorption of uranyl

Nitrogen enrichment and increased nitrogen content is an effective strategy for enhancing adsorption of uranium by carbon nitride polymers. Herein, we reported the uranium absorption by using a structurally well-defined and nitrogen-rich carbon nitride polymer with C3N5 stoichiometry for the first time. In comparison with the adsorption performance of g-C3N4 for U(VI), the conjugation system of the material was increased by connecting the heptazine unit through the azo bridge in the structure of C3N5, so that C3N5 exhibited several times higher adsorption performance than that of g-C3N4. The C3N5 has high kinetics for uranyl ions, which can adsorb 100 mg/g U(VI) in only 10 min and reach complete adsorption equilibrium in 60 min; the theoretical maximum adsorption capacity is 207 mg/g, meanwhile, the material exhibits high selectivity. The results of spectral analysis and theoretical calculations indicate that the process of uranyl ion capture by C3N5 is a combination of physical and chemical adsorption, and its higher density of electronic states makes the electrostatic binding ability enhanced, which is favorable to the adsorption of uranyl ions by C3N5. This work indicates that C3N5 has great promise and application in the separation and enrichment of uranyl ions, and also provides a reference for the systematic investigation of the adsorption ability of nitrogen-rich carbon nitrogen polymers on uranyl ions.

Deformation Performance Analysis of a Truss Structure Based on the Deformation Decomposition Method

Trusses are among the basic components of large-span bridges and large-space structures. A method is proposed to conduct a comprehensive deformation analysis of a truss in terms of the basic rigid body displacements and the tension and compression deformation based on complete mathematical orthogonality and mechanical equilibrium. The correctness of the proposed method is verified by comparison with a traditional strain analysis. Furthermore, a relative deformation decomposition of the mode shape is proposed to analyse in detail its relative displacement and deformation. The correctness and superiority of the proposed method are verified by comparison with the modal mass participation coefficient method and the animation from observation method. Additionally, the relative deformation decomposition of a plane truss structure is realized under any load conditions based on the superposition of mode shapes. The quantitative analysis of the basic deformation performance of a plane truss structure can also be conducted by countable mode shapes, which do not involve load conditions. Finally, the number of mode shapes that must be considered differs when using the maximum displacement and the tension and compression deformation analysis indicators.

Phase Diagrams of Me-O-C Systems to Study Metallurgical Processes

Metallurgical processes in Me-O-C systems cannot be studied and controlled using conventional analytical and physicochemical techniques. This is due to the complex physical and chemical interactions occurring in high-temperature metallurgical systems with the formation of various compounds. To study such processes, mathematical (thermodynamic) simulation and other techniques are widely used, among which graphical diagrams illustrating the equilibrium between individual phases or their systems occupy a special place. Diagrams have been proposed that are more common, informative, and herewith universal to study pyrometallurgical processes. The main research objective was to determine the equilibrium composition of the Me-O-C system, i.e., the amount or ratio of its various compounds such as carbides, oxides, pure substances, and, possibly, ternary compounds. The equilibrium compositions of the system were obtained to plot diagrams from not only experimental studies but also the chemical equilibria mathematical simulation results using the Selector software package. The diagrams proposed herein allow establishing a quantitative relationship between the temperature, the ratio of independent components (metal, oxygen, and carbon), on the one hand, and the complete equilibrium composition of the system, which implies data on the amount and type of condensed and gas phases in the system and their ratios, on the other hand. This mechanism is a new tool to study chemical conversions in complex metallurgical processes, which will be very useful for metallurgists, chemists, and technologists.

Blockchain's role in e-commerce sellers' decision-making on information disclosure under competition.

In e-commerce, sellers can disclose product information (such as quality, size information, function, and so on) to make consumers understand the products. However, in the process of information disclosure, consumers often fall into information distortion or information loss. Because of its immutability and traceability, blockchain can help e-commerce sellers improve information disclosure and ensure the efficiency of information transmission. We study a duopoly competitive e-commerce market in which two e-commerce sellers compete in information disclosure. According to whether to apply blockchain, we divide the sellers’ decision-making into four research scenarios (NN, BN, NB, BB). Based on the above four scenarios, we get the market demand of different products depending on the consumer utility, and further establish the game model in the competitive environment. This paper explores the impact of blockchain on information disclosure and consumer surplus, and achieves the Nash equilibrium of blockchain application for both sides. In the expansion model, we study e-commerce sellers’ risk aversion and capital constraints, and further explore their impact on blockchain in practice. Finally, combining with blockchain’s characteristics, we also analyze the impact of the application of blockchain at other aspects on the supply chain. We find that when consumers' trust in information is low or the cost of blockchain applications is low, all e-commerce sellers in competition will adopt blockchain. In addition, when consumers have low trust in information, it will be difficult to achieve complete equilibrium in the application of blockchain as their risk aversion increases. For capital constrained sellers, when the cost of blockchain application is low, it will be difficult to achieve full equilibrium for blockchain applicants as the bank financing rate increases.

Research on the Trust Mechanism of Individual Consumers in Rural Financial Markets Based on the Dynamic CGE Model

In order to obtain the complete equilibrium state of rural financial market and ensure the stable development of rural financial consumer market, this paper introduces CGE model and analyzes the dynamic trust mechanism of individual consumers in rural financial market. In this paper, the single variable evolutionary fuzzy clustering algorithm is used to analyze the orthogonal eigenvector solutions of individual consumers; the big data of individual consumers under the mode of perceived trust is automatically clustered, so as to obtain the fuzzy analogy function of individual consumers in the rural financial market; and finally the prediction value of consumer trust is obtained. The results show that trust, customer satisfaction, and service quality are positively correlated. Under the same sample expectation constraints, the dynamic CGE model is more robust, and the individual consumer trust mechanism of rural financial market in the study area has higher advantages.

Multiplicity dependence of freezeout scenarios in pp collisions at s=7 TeV

The data on transverse momentum integrated hadron yields in different multiplicity classes of $p+p$ collisions at $\sqrt{s}=7$ TeV have been analyzed to extract the chemical freeze-out parameters using a thermal model. The chemical freeze-out parameters have been extracted for three different freeze-out schemes: (i) unified freeze-out for all hadrons in complete thermal equilibrium (1CFO), (ii) unified freeze-out for all hadrons with an additional parameter ${\ensuremath{\gamma}}_{S}$ which accounts for possible out-of-equilibrium production of strange hadrons ($1\mathrm{CFO}+{\ensuremath{\gamma}}_{S}$), and (iii) separate freeze-out for hadrons with and without strangeness content (2CFO). It has been observed that the $1\mathrm{CFO}+{\ensuremath{\gamma}}_{S}$ scheme gives the best description of the hadronic yields at midrapidity when multiplicity ($\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}$) of the collision is less than 10. This indicates that the strangeness is out of equilibrium in most of the multiplicity classes of $p+p$ collisions. All three parameters of this CFO scheme, temperature $T$, radius $R$ of the fireball, and strangeness suppression factor ${\ensuremath{\gamma}}_{S}$ increase with the increase of $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}$. Furthermore, we have compared applicability of different CFO schemes considering two more colliding systems $p+\text{Pb}$ at $\sqrt{{s}_{\mathrm{NN}}}=5.02$ and $\text{Pb}+\text{Pb}$ at $\sqrt{{s}_{\mathrm{NN}}}=2.76$ TeV along with $p+p$ collisions at $\sqrt{s}=7$ TeV. We observe a freeze-out volume (or multiplicity) dependence of CFO schemes regardless of colliding ions. The $1\text{CFO}+{\ensuremath{\gamma}}_{S}$, 1CFO, and 2CFO schemes provide the best description of the data when the dimensionless quantity $V{T}^{3}$ approximately satisfies the conditions $V{T}^{3}<50, 50<V{T}^{3}<100$, and $V{T}^{3}>100$, respectively, or the corresponding multiplicity satisfies the conditions $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}<30, 30<d{N}_{ch}/d\ensuremath{\eta}<60$, and $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}>100$, respectively.

Nickel isotope fractionation during precipitation of Ni secondary minerals and synchrotron-based analysis of the precipitates

The determination of fractionation factors associated with important biogeochemical processes controlling Ni availability in the environment is necessary to confidently use Ni isotope signatures as tracers in environmental studies. In this paper we present experimental results on Ni isotope fractionation during the precipitation of Ni secondary minerals (Ni hydroxide, Ni hydroxycarbonate and Ni sulfide minerals) that can control Ni fate and mobility in settings where high dissolved Ni(II) concentrations may pose a serious threat to the environment. Results show a preferential partition of lighter isotopes into the solid phase with associated fractionation factors ε of −0.40‰ ± 0.04‰, −0.50‰ ± 0.02‰, and −0.73‰ ± 0.08‰ relative to the hydroxide, carbonate and sulfide systems, respectively. Early kinetically induced isotope fractionation, followed by possible re-equilibration with the reacting solutions was suggested for the three investigated systems. Distortions of Ni-O bonds in the octahedra constituting the structures of Ni hydroxide and hydroxycarbonate minerals could have also contributed to the isotopic fractionation measured in these systems. In contrast, for Ni sulfide system, the magnitude of Ni isotope fractionation seemed to be determined by water and sulfide ligands exchange in solution prior to mineral nucleation. Although there is insufficient evidence to determine whether complete equilibrium occurred in the three studied systems, the fractionation factors reported in this study can provide useful indicators of Ni isotope fractionation associated with fast precipitation of secondary minerals involved in the sequestration of Ni from contaminated environments. These findings also contribute to the characterization of Ni isotope systematics which is still in the early stages of development.

NonMarkovianity in cosmology: Memories kept in a quantum field

In this work we ask how an Unruh–DeWitt (UD) detector with harmonic oscillator internal degrees of freedom Q measuring an evolving quantum matter field Φ(x,t) in an expanding universe with scale factor a(t) responds. We investigate the detector’s response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector W, the ‘Witness’, which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detector’s Q by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector D introduced at late times, called the ‘Detective’, decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics a(t). How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under continuous driving, as in an evolving spacetime, actually helps to retain the memory. We discuss interesting features and potentials of this ‘archeological’ perspective toward cosmological issues.

Quantification of the temperature equilibrium time of the cavity in parallel-plate-type ionization chambers by thermal analysis.

Temperature corrections are necessary to account for the varying mass of air in the cavity volume of a vented ionization chamber. The temporal response resulting from temperature changes in a cylindrical and/or Farmer-type ionization chamber, which is the standard dosimeter, has been thoroughly discussed by some researchers. The purpose of this study was to characterise and analyse the dependence of the cavity air temperature of the parallel-plate-type ionization chamber on changes in the ambient temperature. Ionization chambers NACP-02 (IBA Dosimetry, GmbH) and Advanced Markus TN34045 (PTW, Freiburg) were modelled using thermal analysis software to present the temperature equilibrium time and the entire ionization chamber temperature distribution. The temporal response of each ionization chamber was measured for comparing the calculation results of the thermal analysis. The ionization chamber cavities of NACP-02 and TN34045 reached complete equilibrium in 670 and 750 s, respectively. Heat transfer occurred faster at the centre of the front wall of TN34045 than at the outside of the centre except for the edges. Further, the non-uniformity of temperature in the cavity was in the range of 24.2–24.8°C for NACP-02 and 23.7–24.4°C for TN34045 at 200 s after the ionization chamber was installed in the water phantom. The previous proposal to wait for about 15 mins after submerging the chamber in a water phantom before the measurement is demonstrated to be appropriate for parallel-plate-type ionization chambers.

Centrality Dependence of Chemical Freeze-Out Parameters and Strangeness Equilibration in RHIC and LHC Energies

We have estimated centrality variation of chemical freeze-out parameters from yield data at midrapidity of π ± , K ± and p , p ¯ for collision energies of RHIC (Relativistic Heavy Ion Collider), Beam Energy Scan (RHIC-BES) program, and LHC (Large Hadron Collider). We have considered a simple hadron resonance gas model and employed a formalism involving conserved charges ( B , Q , S ) of QCD for parameterization. Along with temperature and three chemical potentials ( T , μ B , μ Q , μ S ), a strangeness undersaturation factor ( γ S ) has been used to incorporate the partial equilibration in the strange sector. Our obtained freeze-out temperature does not vary much with centrality, whereas chemical potentials and γ S seem to have a significant dependence. The strange hadrons are found to deviate from a complete chemical equilibrium at freeze-out at the peripheral collisions. This deviation appears to be more prominent as the collision energy decreases at lower RHIC-BES energies. We have also shown that this departure from equilibrium reduces towards central collisions, and strange particle equilibration may happen after a threshold number of participants in A - A collision.

Second Law of Thermodynamics, Gibbs’ Thermodynamics, and Relaxation Times of Thermodynamic Parameters

The relationship between the second law of thermodynamics and Gibbs’ thermodynamics is discussed. The second law of thermodynamics is formulated more generally than Gibbs’ thermodynamics, which considers only strictly equilibrium values of thermodynamic functions. Gibbs’ approach generalizes the statistical mechanical theory of equilibrium for thermodynamic variables, except for the difference between the periods of relaxation of all thermodynamic parameters. For small systems, this approach consists of replacing the real physical nature of systems with the stratification of coexisting phases using a model with an interface of mobile phases in contact with a foreign (nonequilibrium) body. For solids, this results in confusion of concepts of the complete phase equilibrium of a system and the mechanical equilibrium of a deformed solid. These two problems are revealed using the molecular kinetic theory of condensed phases, ensuring a self-consistent description of three aggregate states and their interfaces. This theory allows the concepts of the times of the onset and completion of forming entropy in the considered system to be introduced. Allowing for experimental data on the ratios between the measured periods of relaxation for momentum, energy, and mass transfer processes in considering real processes not only ensures a solution to the two problems noted above; it also testifies to the redundancy of the Caratheodory mathematical theory to substantiate the introduction of entropy into multicomponent mixtures. A microscopic interpretation of the formation of entropy in closed systems is given that illustrates the essence of processes preceding the emergence of the reaction completeness parameter in de Donder and Prigogine approaches. Systems in which allowing for periods of relaxation alters existing theories are discussed.

Influence of numerical resolution on the dynamics of finite-size particles with the lattice Boltzmann method.

We investigate and compare the accuracy and efficiency of different numerical approaches to model the dynamics of finite-size particles using the lattice Boltzmann method (LBM). This includes the standard bounce-back (BB) and the equilibrium interpolation (EI) schemes. To accurately compare the different implementations, we first introduce a boundary condition to approximate the flow properties of an unbounded fluid in a finite simulation domain, taking into account the perturbation induced by a moving particle. We show that this boundary treatment is efficient in suppressing detrimental effects on the dynamics of spherical and ellipsoidal particles arising from the finite size of the simulation domain. We then investigate the performances of the BB and EI schemes in modeling the dynamics of a spherical particle settling under Stokes conditions, which can now be reproduced with great accuracy thanks to the treatment of the exterior boundary. We find that the EI scheme outperforms the BB scheme in providing a better accuracy scaling with respect to the resolution of the settling particle, while suppressing finite-size effects due to the particle discretization on the lattice grid. Additionally, in order to further increase the capability of the algorithm in modeling particles of sizes comparable to the lattice spacing, we propose an improvement to the EI scheme, the complete equilibrium interpolation (CEI). This approach allows us to accurately capture the boundaries of the particle also when located between two fluid nodes. We evaluate the CEI performance in solving the dynamics of an under-resolved particle under analogous Stokes conditions and also for the case of a rotating ellipsoid in a shear flow. Finally, we show that EI and CEI are able to recover the correct flow solutions also at small, but finite, Reynolds number. Adopting the CEI scheme it is not only possible to detect particles with zero lattice occupation, but also to increase up to one order of magnitude the accuracy of the dynamics of particles with a size comparable to the lattice spacing with respect to the BB and the EI schemes.

In-Vessel Headspace Liquid Phase Microextraction Coupled to Spectrophotometry for Iodate Determination

A new, highly sensitive and selective method for the spectrophotometric determination of iodate is developed based on the in-vessel mode of headspace liquid phase microextraction (IV-HS-LPME). The approach involves converting iodate to vapor iodine with excess of iodide and extracting it into a 50 μL of 1 % potassium iodide, which exposed to the headspace in a specially designed vessel. The extraction proceeds from 8 mL of aqueous solution containing 0.24 mmol L-1 of iodide and 0.5 mol L-1 of Na2SO4 after injection of 2 mL of 25 % H2SO4. The complete equilibrium is established after the aqueous solution stirred at 1200 rpm for 20 minutes. After that, the triiodide complex formed in the acceptor phase is withdrawn with a microsyringe and transferred to a 50 μL quartz micro cell with a 10 mm path length, where the absorbance is measured at 288 or 350 nm. The calibration graph is linear (r2 = 0.9998) in the range of 4 to 180 μg L-1 (as IO3-) with a detection limit of 1.5 μg L-1. The developed method has a high precision of 0.5 – 1.4 %. It was successfully applied to the determination of iodate in table salt, sea, and mineral water samples.

Chemical composition and sorption properties of lignocellulosic complexes of fruit seed shells and walnut shells

We investigated chemical composition and sorption properties of lignocellulosic complexes of wastes of agroindustrial complex, namely crushed shells of apricot, cherry and peach seeds, and walnut shells. Chemical analysis revealed that walnut shells show the highest content of polysaccharide components. Cherry and peach seed shells are characterized by a higher content of aromatic components (lignin). Based on the results of sorption of benzene vapor, the following sequence of the volumes of adsorption pores was found: walnut shells (0.03 cm3 g–1)=apricot seed shells (0.03 cm3 g–1)>peach seed shells (0.02 cm3 g–1)>cherry seed shells (0.01 cm3 g–1). The sorption capacity of biosorbents towards methylene blue was investigated as a function of pH of an aqueous solution, process duration, and initial dye concentration. It was established that the maximum efficiency of sorption is achieved at pH 6, while the minimum value corresponds to low pH values. Probably, an increase in pH value leads to deprotonation of carboxyl groups of biosorbents followed by changes in their surface charge into negative. This causes a decrease in electrostatic repulsion forces between the positively charged dye cation and the surface of the biosorbents. Therefore, the sorption centers are formed. The data on kinetics of sorption showed that during the first 30 min of contact the absorption of 55–60% of the dye cations occurs on the biosorbents, whereas complete sorption equilibrium is achieved within 120–180 min. The following sequence of the sorption capacity of lignocellulosic materials towards methylene blue was established: apricot seed shells (43.9 mg g–1)>walnut shells (37.8 mg g–1)>peach seed shells (30.1 mg g–1)>cherry seed shells (26.5 mg g–1). The Freundlich isotherm is the most suitable for describing the cationic dye absorption by biosorbents, and the calculated values are in good agreement with the experimental data.

Cell size influences inorganic carbon acquisition in artificially selected phytoplankton.

Cell size influences the rate at which phytoplankton assimilate dissolved inorganic carbon (DIC), but it is unclear whether volume-specific carbon uptake should be greater in smaller or larger cells. On the one hand, Fick's Law predicts smaller cells to have a superior diffusive CO2 supply. On the other, larger cells may have greater scope to invest metabolic energy to upregulate active transport per unit area through CO2 -concentrating mechanisms (CCMs). Previous studies have focused on among-species comparisons, which complicates disentangling the role of cell size from other covarying traits. In this study, we investigated the DIC assimilation of the green alga Dunaliella tertiolecta after using artificial selection to evolve a 9.3-fold difference in cell volume. We compared CO2 affinity, external carbonic anhydrase (CAext ), isotopic signatures (δ13 C) and growth among size-selected lineages. Evolving cells to larger sizes led to an upregulation of CCMs that improved the DIC uptake of this species, with higher CO2 affinity, higher CAext and higher δ13 C. Larger cells also achieved faster growth and higher maximum biovolume densities. We showed that evolutionary shifts in cell size can alter the efficiency of DIC uptake systems to influence the fitness of a phytoplankton species.

Isogeometric nonlinear bending and instability analysis of cylindrical composite shells reinforced with graphene platelets

In the present study, by using IGA (isogeometric analysis) method, the nonlinear bending and instability behavior of cylindrical composite shells embedded with GPLs (graphene platelets) having functional gradation is investigated. In IGA, NURBS functions are employed both to construct the geometry and to approximate the field variables. Advantages of adopting IGA include: the exact geometrical description, high accuracy and efficacy, higher-order smoothness. The nonlinear equations of equilibrium are derived via the virtual work principle on the basis of a higher-order shell theory with the large deflection. A solution procedure in which the arc length method is modified and exploited in combination with the modified Newton-Raphson method for the highly nonlinear problem is designed to trace accurately the nonlinear equilibrium path that encompasses the snap-through and snap-back phenomena. Four patterns of the GPL dispersions are prepared: uniform, O-type, X-type and A-type, and evenly distributed and central point loadings are considered. The proposed IGA approach is evidenced to successfully capture the complete nonlinear equilibrium path of the composite shell under flexure. The further parametric examinations that follow to highlight the impacts of the loading and constraint conditions, GPL weight fraction, reinforcement schemes and shell geometric parameter on the nonlinear bending and instability responses.

Dynamics of a Virological Model for Cancer Therapy with Innate Immune Response

The aim of this work is to present a virological model for cancer therapy that includes the innate immune response and saturation effect. The presented model combines both the evolution of a logistic growing tumor and time delay which stands for the period of the viral lytic cycle. We use the delay differential equation in order to model this time which also means the time needed for the infected tumor cells to produce new virions after viral entry. We show that the delayed model has four equilibria which are the desired outcome therapy equilibrium, the complete failure therapy equilibrium, the partial success therapy free-immune equilibrium when the innate immune response has not been established, and the partial success therapy equilibrium with immune response. Furthermore, the stability analysis of equilibria and the Hopf bifurcation are properly exhibited.

Depression and Yoga A review

Yoga is a system of physical and mental self-improvement and final liberation that people have been using for thousands of years. Yoga is a science which is common to all and whole humanity in its true nature of efficacy, results and applications. Yoga is a centuries-old guide to healthy living developed by ancient Indian sages. With its unique blend of physical exercises, psychological insight, and philosophy, it can help you to bring your body, mind, and spirit into better balance. Yoga takes a holistic approach to life, enabling you to experience complete equilibrium inside and out. Depression is one of the most common mental illnesses in the world. It is estimated that there are 350 million people worldwide who have some form of depression. Indians are among the worlds most depressed, according to a (WHO) World Health Organization-sponsored study. So to addressing such type of huge problem in present scenario we have to take help of yoga and mind relaxing technique. Present study intended to review research work has been performed on using yoga to alleviate depression. This review will focus on how yoga is being useful to treat depression. Findings from this review will be used to determine areas of further study and implications for clinical social work practice.