Exposure to persistent organic pollutants and thyroid cancer risk: a study protocol of systematic review and meta-analysis

INTRODUCTION

The thyroid cancer incidence has been increasing all over the world. However, the aetiology of thyroid cancer remains unclear. A growing body of evidence suggested exposure to persistent organic pollutants (POPs) may play a role in the initiation of thyroid cancer, but the results are generally inconsistent across studies. This review aims to synthesise the evidence for the health effects of POPs on the risk of thyroid cancer.

METHODS AND ANALYSIS

This protocol was reported in accordance to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA) statements. A comprehensive search, including electronic database search (eg, PubMed, Embase, ProQuest and CNKI), website search and manual search, will be performed to identify all eligible studies. The Population, Exposure, Comparator and Outcome framework was used to clarify the inclusion and exclusion criteria. The Newcastle-Ottawa Scale will be used to assess the quality of included studies. Maximally adjusted effect estimates from individual studies will be summarised with random-effect models in a conservative manner. I² statistics and Q-tests will be used to test the heterogeneity across studies. We will perform extensive sensitivity analyses, such as confounding risk ratio (confounding), E-value, fixed-effect models, excluding the most relatively weighted study, including only the high-quality studies and many predesigned subgroup analyses, etc. The findings will be reported in accordance to the PRISMA guidelines.

ETHICS AND DISSEMINATION

Ethical approval is not required in this systematic review of published literatures. The results will be published in a peer-reviewed journal and presented at relevant conferences.

PROSPERO REGISTRATION NUMBER

CRD42020181343.

[Progress of researches on the use of ultrasound in the diagnosis and treatment of hepatic alveolar echinococcosis]

The patients with hepatic alveolar echinococcosis have unapparent early symptoms due to invasive and slow growth, and the disease is usually at an advanced stage upon diagnosis, which has a poor prognosis. Early diagnosis of hepatic alveolar echinococcosis is therefore of great importance. The advances in the ultrasound techniques continues to improve the accuracy for the diagnosis of hepatic alveolar echinococcosis, and ultrasound plays a critical role in the treatment and assessment of therapeutic efficacy for hepatic alveolar echinococcosis. This paper mainly reviews the application of ultrasound in the diagnosis and treatment of hepatic alveolar echinococcosis.

[Polymorphism analysis of MTHFR，BMPR1B and TYMS in microtia]

Objective:To explore the relationship between MTHFR，BMPR1B and TYMS polymorphism and congenitial microtia in Chinese Han population.Method:A total of 180 microtia patients and 141 healthy participants were enrolled in this study.The genotyping of MTHFR rs4846049, BMPR1B rs1434536 and TYMS rs2790 of the participants were examined with multiple PCR. Frequencies and allele distribution of MTHFR rs4846049,BMPR1B rs1434536 and TYMS rs2790 between cases and control were analyzed with Chi-square test. Result:The genotype frequency distribution of TYMS rs27901 polymorphism was significantly different between two groups(P<0.05).Furthermore, gender stratified analysis showed that TYMS rs2790 polymorphism mainly increase the risks of congenitial microtia in male(P<0.05).Compared with AA genotype,the mircotia risks of subjects with AG GG AG+GG raised to 1.93, 3.23 and 2.10 times,respectively(95%CI:1.07-3.48、1.12-9.33 and 1.20-3.68).However,there was no relationship between MTHFR rs4846049, BMPR1B rs1434536 and microtia. Conclusion:The TYMS rs2790 polymorphism may be a risk factor of microtia in male.

Vitamin E promotes breast cancer cell proliferation by reducing ROS production and p53 expression

OBJECTIVE

The role of antioxidant in cancer cell proliferation is still controversial. This study aimed to explore the effects of antioxidant vitamin E on the proliferation of breast cancer cells and the possible underlying mechanisms.

MATERIALS AND METHODS

Orthotopic breast cancer model was established by inoculating MCF7 cells in mice and in vitro MCF7 culture system. CM-H2DCFDA fluorescence probe and Western blot analysis were used to detect ROS changes and p53 expression. p53 knockdown in MCF7 cells by siRNA transfection was also used to determine the combination effect of vitamin E and p53 on MCF7 cell proliferation.

RESULTS

Vitamin E supplement in the chow significantly accelerated breast cancer cell growth in vivo. ROS level and p53 expression were decreased in tumor tissues. Water-solvable vitamin E Trolox significantly promoted MCF7 cell proliferation in vitro, while reducing intracellular ROS level and p53 expression. p53 knowdown by p53-siRNA transfection inMCF7 cells significantly reduced p53 expression and increased MCF7 cell proliferation.

CONCLUSIONS

Vitamin E accelerated breast cancer growth by reducing ROS production and p53 expression.

[Diagnostic values of mitral inflow and mitral annulus diastolic velocity for heart failure with preserved ejection fraction]

OBJECTIVE

To explore the diagnostic values of ratios of early diastolic peak transmitral velocity(E) to late velocity(A) (E/A) and E to early diastolic peak mitral annulus velocity (E/E') for heart failure patients with preserved ejection fraction (HF-PEF).

METHODS

Two hundred and sixteen healthy people were divided into <50 years, 50-59 years, 60-69 years, and ≥70 years groups to clarify the impact of aging on E/A and E/E'. Two hundred and two newly diagnosed consecutive in-patients with HF-PEF and 221 age- and sex-matched non-heart-failure subjects with risk factors of HF-PEF (negative controls) were enrolled.The diagnostic values and cutoff points of E/A and E/E' for HF-PEF were derived from receiver operating characteristic curve (ROC) analysis.

RESULTS

E/A and E/E' were significantly different among age groups in healthy controls (all P<0.01). Compared with <50 years group, average E/A was lower and average E/E' was higher in ≥70 years group(both P<0.01). E/A ratio was less than 1 in 68%(71/105), E/E' was >8 cm/s in 48% (50/105)healthy people with age≥60 years. Neither E/A nor E/E' of HF-PEF patients was statistically different regarding to NYHA classification (grade Ⅱ, Ⅲ, Ⅳ), but NT-proBNP value increased in proportion to higher NYHA classification(P<0.01). The area of E/E' under ROC for diagnosing HF-PEF was 0.839(P<0.01), and the corresponding cutoff point was 9.5 with a sensitivity of 86% and a specificity of 69%. The areas of E/A (larger value or smaller value indicating positive) under ROC for diagnosing HF-PEF were 0.469 and 0.531, respectively(all P>0.05).

CONCLUSIONS

Aging exerts significant impacts on both E/A and E/E'. E/E' has moderate diagnostic accuracy while E/A is of limited value for diagnosing HF-PEF.

Optical spectroscopy of PPV-based block copolymers of nanostructured supramolecular organic semiconductor

The third-order nonlinearity of a PPV-based nanostructured supramolecular organic semiconductor (DBAB), with an electron donor (D) connected to an electron acceptor (A) via nonconjugated and flexible bridge (B) units, was investigated in this work at both near-resonant (532 nm) and nonresonant (1064 nm) wavelength by using degenerate four-wave mixing. The second hyperpolarizabilities of D, A, and DBAB at 532 nm were found to be approximately 2.42 x 10(-43) m2/V2, 7.75 x 10(-44) m2/V2, and 1.80 x 10(-43) m2/V2 in copolarization geometry, and approximately 1.59 x 10(-43) m2/V2, 2.59 x 10(-44) m2/V2, and 1.18 x 10(-43) m2/V2 in orthogonal polarization geometry, respectively. The second hyperpolarizabilities of DBAB at 1064 nm were approximately 1.66 x 10(-46) m2/V2 and approximately 8.77 x 10(-47) m2/V2 for parallel and orthogonal polarization cases.

Nonlinear optical properties of mushroom-shaped CdSe/CdS coreshells

The third-order nonlinear optical susceptibilities of mushroom-shaped CdSe/CdS coreshells as a function of concentration have been investigated using polarization- and concentration-resolved degenerate four-wave mixing in a resonant region. The effective third-order nonlinear optical susceptibilities, /chi(3)xxxx/ and /chi(3)xyyx/ of CdSe/CdS coreshells were estimated to be approximately 1.86 x 10(-21)-1.03 x 10(-20) m2/V2, and approximately 0.45 x 10(-21)-6.15 x 10(-21) m2/V2, respectively, for various concentrations of approximately 0.64 x 10(-3)-4.95 x 10(-3) mol/m3. The second hyperpolarizabilities, /<gammah>xxxx/ and /<gammah>xyyx/, of CdSe/CdS coreshells were extracted to be approximately 2.37 x 10(-41) m5/V2 and approximately 1.29 x 10(-41) m5/V2, respectively.

Anesthesia cutoff phenomenon: interfacial hydrogen bonding

Anesthesia "cutoff" refers to the phenomenon of loss of anesthetic potency in a homologous series of alkanes and their derivatives when their sizes become too large. In this study, hydrogen bonding of 1-alkanol series (ethanol to eicosanol) to dipalmitoyl-L-alpha-phosphatidylcholine (DPPC) was studied by Fourier transform infrared spectroscopy (FTIR) in DPPC-D2O-in-CCl4 reversed micelles. The alkanols formed hydrogen bonds with the phosphate moiety of DPPC and released the DPPC-bound deuterated water, evidenced by increases in the bound O-H stretching signal of the alkanol-DPPC complex and also in the free O-D stretching band of unbound D2O. These effects increased according to the elongation of the carbon chain of 1-alkanols from ethanol (C2) to 1-decanol (C10), but suddenly almost disappeared at 1-tetradecanol (C14). Anesthetic potencies of these alkanols, estimated by the activity of brine shrimps, were linearly related to hydrogen bond-breaking activities below C10 and agreed with the FTIR data in the cutoff at C10.

Infrared spectra of phospholipid membranes: interfacial dehydration by volatile anesthetics and phase transition

Fourier-transform infrared attenuated total reflection (ATR) spectroscopy was used to study the effect of volatile anesthetics on fully hydrated dipalmitoylphosphatidylcholine (DPPC) vesicle membranes. The main phase transition was monitored by the change in the C-H2 asymmetric stretching frequencies of the lipid tails. The surface property was analyzed by the changes in the P = O stretching, (CH3)3-N+ stretching of the hydrophilic head, and C = O stretching of the glycerol skeleton. The partial pressures of those agents that decreased the transition temperature 1.0 C degree were halothane 0.75, enflurane 1.90 and CCl4 0.85 kPa. At a 2:1 lipid/anesthetic mole ratio, the polar anesthetics, halothane and enflurane, increased the ratio of (P = O stretching band area)/((CH3)3-N+ stretching band area) by 26.3% and 21.1%, respectively, whereas apolar CCl4 increased it 10.5%. The water molecules bound to the P = O moiety are apparently replaced by the anesthetic molecules. The deconvoluted C = O spectra showed two peaks: free sn-1 that is closer to the lipid core and hydrogen-bonded sn-2 that is closer to the polar head. Addition of halothane and enflurane, but not CCl4, increased the number of peaks to three. The third peak is free sn-2, formed by disrupting hydrogen-bonding to water. Because the temperature-induced spectral change was limited to C-H2 stretching at the main phase transition, the effects of anesthetics on the lipid membrane structure are not identical to temperature elevation. Among anesthetics, the effects of apolar and polar molecules on the interfacial properties are different.

Membrane-buffer partition coefficients of tetracaine for liquid-crystal and solid-gel membranes estimated by direct ultraviolet spectrophotometry

The membrane-buffer partition coefficient of tetracaine was measured by direct ultraviolet spectrophotometry in dimyristoylphosphatidylcholine unilamellar liposomes at temperatures above and below the main phase transition. The partition coefficients of uncharged tetracaine to solid-gel (18 degrees C) and liquid-crystal (30 degrees C) membranes were 6.9 x 10(4) and 1.2 x 10(5), respectively. Despite the general assumption that local anesthetic binding to the solid membrane is negligible, this study showed that the solid membrane binding amounts to 57.5% of the liquid membrane binding. Binding of the charged form to the liquid or solid membrane was not detectable under the present experimental condition of 0.03 mM tetracaine bulk concentration. The present method measures metachromasia of local anesthetics when bound to lipid membranes. Its advantage is that the separation of the vesicles from the solution is not required. A linearized equation is presented that estimates the partition coefficient or binding constant graphically from a linear plot of the absorbance data. The method is applicable for estimation of drug partition when a measurable spectral change occurs due to complex formation.

Fourier transform infrared studies on phospholipid hydration: phosphate-oriented hydrogen bonding and its attenuation by volatile anesthetics

Water-phospholipid (dimyristoylphosphatidylcholine) interaction was analyzed in a water-in-oil(benzene) reversed micellar system using Fourier transform infrared spectroscopy, and the effects of inhalation anesthetics (halothane, enflurane, chloroform, and carbon tetrachloride) on the interaction were studied. The O-H stretching frequency, representing water, increased from 3369 cm-1 to a steady 3430 cm-1 when the water/phospholipid mole ratio exceeded 18. The value did not quite reach the frequency of free water of 3490 cm-1 at the water/phospholipid mole ratio of 30. The O-H bending frequency of water did not appear until the water/phospholipid mole ratio exceeded 9. The P=O stretching frequency in the polar head group of unhydrated dimyristoylphosphatidylcholine was 1262 cm-1 and decreased with the addition of water, reaching a steady value of 1238 cm-1 at the water/phospholipid mole ratio of 9. However, the (CH3)3N+ stretching of the choline head, as well as the C-H stretching of the hydrocarbon tail and the C=O stretching of the ester linkage, showed little change by the addition of water. The present results suggest that the primary hydration site of dimyristoylphosphatidylcholine is the phosphate moiety, and up to 18 water molecules are restricted at the polar head group. Apparently, the choline head has a minor role in the hydration of phospholipids despite the positive electrostatic charge. Among the water molecules interacting with the phospholipid head group, about 9 water molecules are strongly bound. The water content in the micelles correlated linearly with the ratio of the absorbance band area between O-H and C=O stretching. The addition of polar anesthetics (halothane, enflurane, and chloroform) increased the O-H stretching frequency and elevated the ratio of the absorbance band area between O-H and C=O stretching, implying that the anesthetics released the structured water molecules bound at the phospholipid-water interface. The anesthetics disrupted the hydrogen bond between the phosphate moiety of the phospholipid and water. Although apolar carbon tetrachloride also released bound water molecules, the magnitude was less than that of the polar anesthetics, as expected. The anesthetics did not affect the C-H stretching or C=O stretching bands, indicating that the disordering action upon the hydrocarbon core of phospholipid membranes is minimal at low water content. These results support our view that the primary site of action of inhalation anesthetics is the membrane-water interface, releasing bound water molecules.

Dose-dependent nonlinear response of the main phase-transition temperature of phospholipid membranes to alcohols

The effect of 1-alkanols upon the main phase-transition temperature of phospholipid vesicle membranes between gel and liquid-crystalline phases was not a simple monotonic function of alkanol concentration. For instance, 1-decanol decreased the transition temperature at low concentrations, but increased it at high concentrations, displaying a minimal temperature. This concentration-induced biphasic effect cannot be explained by the van't Hoff model on the effect of impurities upon the freezing point. To explain this nonlinear response, a theory is presented which treats the effect of 1-alkanols (or any additives) on the transition temperature of phospholipid membranes in a three-component mixture. By fitting the experimental data to the theory, the enthalpy of the phase transition delta H* and the interaction energy, epsilon*AB between the additive and phospholipid molecules may be estimated. The theory predicts that when epsilon*AB greater than 2 (where epsilon*AB = epsilon AB/RT0, T0 being the transition temperature of phospholipid), both minimum and maximum transition temperatures should exist. When epsilon*AB = 2, only one inflection point exists. When epsilon*AB less than 2, neither maximum nor minimum exists. The alkanol concentration at which the transition temperature is minimum (Xmin) depends on the epsilon*AB value: the larger the epsilon*AB values, the smaller the Xmin. When epsilon*AB is large enough, Xmin values become so small that the plot delta T vs. X shows positive delta T in almost all alkanol concentrations. The interaction energy between 1-alkanols and phospholipid molecules increased with the increase in the carbon chain-length of 1-alkanols. In the case of the dipalmitoylphosphatidylcholine vesicle membrane, the carbon chain-length of 1-alkanols that caused predominantly positive delta T was about 12.

Anesthetics release unfreezable and bound water in partially hydrated phospholipid lamellar systems and elevate phase transition temperature

A dimyristoylphosphatidylcholine multilamellar system with varied water content was prepared by dessiccating sonicated vesicles in vacuo. The water content in the sample was determined by gas chromatography after dissolving the multilamellar system in water-free benzene. Differential scanning microcalorimetry revealed several endothermic peaks in the heating scan at subzero temperature, ranging from -25 to -3 degrees. The peaks that appeared in the subzero temperature range indicate the existence of water molecules bound to the lipid head groups, differing from free water that freezes at 0 degrees. The difference between the amount of water molecules that froze in calorimetry and the total amount of water detected by gas chromatography indicates the presence of unfreezable, tightly bound water molecules. The relative amount of free, intermediate, and unfreezable water was estimated by comparing the differential scanning microcalorimetry data with gas chromatography measurements. The addition of halothane and 1-hexanol significantly decreased the intermediately bound water peaks. The anesthetics dehydrated the lamellar system. The phase polymorphism of partially hydrated phospholipid multilayers is well known, and the temperature that corresponds to the main phase transition of fully hydrated lipid membranes shifts to a higher temperature. The addition of anesthetics increased the phase transition temperature when the water content was less than 18 wt%. This result is the complete reverse of the depressant action of anesthetics in fully hydrated lipid membranes. The present anesthetic effect upon the elevation of the transition temperature is apparently caused by anesthetic-induced dehydration of the lipid-water interface at the present experimental condition.

Frictional torque in surface and conventional hip replacement

The frictional torque of the Trapezoidal-28 total hip replacement and the Tharies SR-3 and SR-5 surface replacements were measured in the University of California at Los Angeles hip-joint simulator in calf serum. Loads of as much as 890 newtons were applied while the femoral component oscillated through a 60-degree arc at forty cycles per minute. Frictional torque, as measured by a ring transducer at a fixed distance from the center of rotation, was seen to diminish as the thickness of the polyethylene increased and was found to be relatively proportional to the diameter of the femoral component. The torques measured in this study were found to be twenty to 100 times smaller than the static torques to failure for acetabular fixation that have been reported in the literature. Finally, no permanent deformation of the thin acetabular shells attributable to the cementing process was apparent when the recommended technique of surgical insertion was utilized.

CLINICAL RELEVANCE

Surface replacement components have been shown to generate greater frictional torques at the acetabular bone-cement interface than do smaller-diameter conventional hip replacements. This indicates that the local mechanical-loading conditions of the hip joint are not the same for both types of replacements, and this should be considered when selecting the type of arthroplasty for an individual patient.

Revision of aseptic loose total hip arthroplasties

Sixty-six patients were revised for aseptic loosening of their conventional hip arthroplasties; follow-up periods ranged from one to nine years. In comparing them with an overall conventional arthroplasty series, there was a higher failure rate with dysplasia and post-traumatic patients, and a lower incidence in osteoarthritic and rheumatoid patients. The average time to revision was four years. The patients were eight years younger than those in the overall UCLA conventional hip arthroplasty series. Forty-two per cent had undergone hip surgery prior to the original hip arthroplasty that failed. The average improvement, as well as the follow-up pain, walking, and function ratings, and the postoperative flexion arc were less than those in the overall conventional arthroplasty series. The quality of femoral and acetabular fixation obtained at revision was considerably inferior to that of the primary surgery. Six patients (9%) have already required re-revision of their hip arthroplasties. In a further 20%, the radiolucencies progressed substantially in extent and width, and are radiographically loose. Although these patients are relatively asymptomatic, prognosis is guarded. Forty-four per cent had no complications and are radiographically well fixed. Other complications included trochanteric migration (7.6%), dislocation (10.6%), and peroneal nerve palsy (7.6%), but there were no deaths or other serious medical complications and only one case (1.5%) of sepsis.

Reaction kinetics in living systems

In this report we treat reaction rates, equilibrium theory, and irreversible thermodynamics as different aspects of a single discipline. In biological reactions the rate is ultimately controlled by enzymes and other proteins of complex structure and high molecular weight. The needed formalism can be placed in one-to-one correspondence with appropriate electrical and mechanical networks. An enzyme molecule has zwitter ions anchored in the polypeptide chain, which enable it to distort the substrate by electrostatic polarization. Water weakens the induced or existing polar bonds and so speeds reaction. Several biological processes, such as luminescence, catalysis, nerve excitation, and anesthesia, in which enzymatic reactions play a major part are discussed from this point of view. We also have discussed the energy consumption and coupling effect in living systems. It is likely that a small fraction of bonds can become energy rich through the process of quenching and that unsymmetrical barriers in biological systems act like transistors in making the driving forces more efficient by a valve effect.

A theory of distortion of the reaction zone

A cylindrical detonating explosive behaves like a non-Newtonian viscous fluid emerging from a cylindrical pipe. The expression for non-Newtonian viscous flow has been applied to detonating explosives. The resultant fit to emerging flame fronts from detonation is excellent for a wide variety of detonating explosives both for transients (at various times) and for steady state. The quantities k ′(λ/λ 1 )(2/ B ) and 1/ B and the rate constant k ′ increase abruptly at a time supporting a change in mechanism from deflagration to detonation in the transient during initiation. All of these parameters are temperature sensitive, indicating an abrupt temperature increase as a condition or indicator in the deflagration-to-detonation transition. Furthermore, a straight line results when log particle velocity u is plotted against log radial distance r , indicating that, for the explosives studied, the hyperbolic cosine wave front can be replaced by a parabolic wave front within the accuracy of the available experimental data.

Similarity and differences between conditions for initiation and failure of detonation

A theory is proposed to study the sensitivity of cylindrical explosives. Using the equations governing the conservation of mass, energy, and momentum, the equation of state, and Newtonian mechanics, we have derived the expression D = D(o)e(-a2/d), in which the apparent length of the reaction zone, a, takes into account burned and unburned explosive and pressure release through the back and sides of the reaction zone. D is the detonation velocity and d is the diameter of the cylindrical charge. From the observed D(1/d) curves and critical energy values, we can interpret failure and other phenomena associated with detonation.

Thermodynamic properties of solid C 2 H 4

The significant structures procedure of liquids has been used to calculate the thermodynamic properties of solid C 2 H 4 . Two degeneracy terms were used to describe the behavior in the vicinities of the two phase transitions. The calculated entropy and specific heat agree well with experimental results from a few kelvins to the melting point. Less satisfactory agreement is obtained for compressibility and thermal expansion coefficients. This simple model represents surprisingly well the phase transitions in the solid state.

Hysteresis effects of C 1 H 4 and C 2 H 4 in the regions of the solid-phase transitions

The thermodynamic model of hysteresis in phase transitions based on the regular solution theory, previously developed, was applied to the solid phases of C 1 H 4 and C 2 H 4 . The width and height of the hysteresis loops for these systems were calculated and compared with the experimental data; agreement was satisfactory.

Single partition function for three phases

The significant structures theory of liquids has been extended to take into account (i) translational degrees of freedom in the degeneracy term and (ii) the perturbation term which becomes important near the critical region. With these improvements, the calculated thermodynamic properties of argon agree very well with experimental results from the melting point through the critical point, along the coexistence curve as well as along the critical isochore and for the solid and the vapor.

Properties of molten magnesium oxide

The Significant Structure Theory of Liquids has been used to calculate the thermodynamic properties, viscosity, self-diffusion coefficient, and specific conductance of molten magnesium oxide, taking account of the decomposition of MgO to Mg and O(2) species in the gas-like part of the partition function.

The significant structure theory applied to a mesophase system

The significant structure theory of liquids is extended to the mesophase system with p-azoxyanisole as an example. This compound has two different structures, a nematic phase and an isotropic phase, in its liquid state. In this study the nematic phase is treated as subject to a second volume and temperature-dependent degeneracy formally like that due to melting. The isotropic phase is treated as a normal liquid. The specific heat, thermal expansion coefficient, compressibility, volume, entropy of transitions, and heat of transitions are calculated and compared to the observed values. This analysis differs from previous ones in including the volume dependence as well as the temperature dependence in one explicit expression for the Helmholtz free energy.

The significant structure theory applied to amorphous and crystalline polyethylene

The significant structure theory of liquids has been applied to amorphous and crystalline polyethylene. In this theory the amorphous state, like liquids in general, is assumed to have solid-like structure, gaslike structure, and positional degeneracy which arises from the motion of kinetic segments and from the libration of CH(2) units. This concept leads to a partition function giving the Helmholtz free energy in terms of volume, temperature, and composition.Thermodynamic and transport properties are calculated for amorphous polyethylene. The thermodynamic properties are also calculated for the crystalline solid. The calculated results are in reasonable agreement with the experimental values. No such detailed calculations of polymer properties from a partition function, depending on both volume and temperature, have been previously attempted.