Measurement of the (p, \rho,T) Properties for Pure Hydrocarbons at Temperatures up to 600 K and Pressures up to 200 MPa

The data available for the thermodynamic properties of propane, \(n\) -butane, and isobutane at temperatures above 440 K are outdated and show significant discrepancies with each other. The ambiguity associated with these data could be limiting to the development of any understanding related to the effects of mixing of these substances with other materials such as \(\text{ CO}_{2}\) , ammonia, and non-flammable or lower-flammable HFC refrigerants. In this study, the (p, \(\rho \) , T) properties of propane, \(n\) -butane, and isobutane were measured at temperatures ranging from (360 to 600) K and pressures ranging from (50 to 200) MPa. Precise measurements were carried out using a metal-bellows variable volumometer with a thermostatted air bath. The expanded uncertainties \((k = 2)\) in the temperature, pressure, and density measurements were estimated to be \(<\) 5 mK, 0.02 MPa, and 0.88 kg  \(\cdot \)  m \(^{-3}\) ( \(T\le 423\)  K, \(p<100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T\le 423\)  K, \(p\ge 100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p < 100\)  MPa), and 2.94 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p \ge 100\)  MPa), respectively. The data obtained throughout this study were systematically compared with the calculated values derived from the available equations of state. These models agree well with the measured data at higher temperatures up to 600 K, demonstrating their suitability for an effective and precise examination of the mixing effects of potential alternative mixtures.     

({p, \rho,T, x}) Properties of \text{ CO}_{2}/Propane Binary Mixtures at 280 K to 440 K and 3 MPa to 200 MPa

The (p, \(\rho \) , T, x) properties of binary mixtures of CO \(_{2}\) (volume fraction purity 0.99999) and propane (mole fraction purity 0.9999) ( \(x_{1}\) CO \(_{2}+x_{2}\) propane; \(x_{1} = 0.1744\) , 0.3863, 0.5837, and 0.7732) were measured in the compressed liquid phase using a metal-bellows variable volumometer. Measurements were conducted from 280 K to 440 K and 3 MPa to 200 MPa. The expanded uncertainties ( \(k = 2\) ) were estimated to be temperature, \(<\) 3 mK; pressure, 1.5 kPa ( \(p\le 7\)  MPa), 0.06 % (7 MPa \(< p\le 50\)  MPa), 0.1 % (50 MPa \(< p\le 150\)  MPa), 0.2 % ( \(p> 150\)  MPa); density, 0.10 %; and composition, \(4.4\times 10^{-4}\) . At \(p >100\)  MPa and 280 K or 440 K, the uncertainties in density measurements increase to 0.14 % and 0.22 %, respectively. The data were compared with available equations of state. The excess molar volumes, \(v_\mathrm{m}^\mathrm{E}\) , of the mixtures were calculated and plotted as a function of temperature and pressure.     

Thermal Stability of \beta -PtO_2 Investigated by Simultaneous Thermal Analysis and Its Influence on Platinum Resistance Thermometry

We present thermogravimetric and differential scanning calorimetric studies of PtO \(_2\) powders measured in different atmospheres. In synthetic air a mass loss of 11.4 % is found at the decomposition temperature \(T_\mathrm {D}\)  = 595  \(^{\circ }\hbox {C}\) which can be attributed to the reduction of PtO \(_2\) . In a helium atmosphere the mass loss is 12.0 % and is found at 490  \(^{\circ }\hbox {C}\) . Subsequent heating in air leads to another oxidation process above \(T_\mathrm {D}\) and a reduction at 800  \(^{\circ }\hbox {C}\) . The second oxidation and reduction process is strongly suppressed when the powder is heated in He. The remaining mass above \(T_\mathrm {D}\) does not comply with a reduction path PtO \(_2 \rightarrow \) PtO \(\rightarrow \) Pt. Differential scanning calorimetry shows an endothermic reaction at \(T_\mathrm {D}\) in synthetic air as well as in helium which corresponds with the mass loss. These measurements imply that the powder can be assigned to be \(\beta \) -PtO \(_2\) . Furthermore, catalytic activity of the PtO \(_2\) powder is evidenced by mass spectrometry to be present below 460  \(^{\circ }\hbox {C}\) . Finally, the impact of these findings on the stability of platinum resistance thermometers is discussed.     

Effective Thermal-Conductivity Measurement on Germanate Glass–Ceramics Employing the 3\omega Method at High Temperature

It can be noted that the germanate glass–ceramic is a functional material with excellent thermal stability which can be used in optical devices. The temperature-dependent effective thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramics from 295.5 K to 780 K are determined using a \(3\omega \) method. One of the main advantages for the \(3\omega \) method is to diminish radiation errors effectively when the temperature is as high as 1000 K. Thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) increase with a rise in temperature. Effective thermal conductivities of a sample increase from \(1.55~\hbox {W}\cdot \hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 295.5 K to \(7.64~\hbox {W}\cdot \,\hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 698.1 K. The effective thermal conductivity of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramic increases with a rise of temperature. This investigation can be used as a basis for the measurement of thermal properties of ceramic materials at higher temperature.     

Development of Superconducting Microresonators for a Neutrino Mass Experiment

The determination of the neutrino mass is still an open issue in particle physics. The calorimetric measurement of the energy released in a nuclear beta decay allows to measure all the released energy, except the fraction carried away by the neutrino: a finite neutrino mass m \(_\upnu \) causes the energy spectrum to be truncated at Q  \(-\)  m \(_\upnu \) , where Q is the transition energy. The electron capture of \(^{163}\) Ho (Q \(\sim \) 2.5 keV) results to be an ideal decay. In order to achieve enough statistics, a large number of detectors ( \(\sim \) 10 \(^4\) ) is required. Superconducting microwave microresonators are detectors suitable for large-scale multiplexed frequency domain readout, with theoretical energy and time resolution of \(\sim \) eV and \(\sim \!\upmu \) s. Our aim is to develop arrays of microresonator detectors applicable to the calorimetric measurement of the energy spectra of \(^{163}\) Ho. Currently, a study aimed to the selection of the best design and material for the detectors is in progress. In this contribution, a comparison between the measurements (critical temperature, gap parameter, quasiparticle recombination time and X-ray energy spectra) made with stoichiometric, sub-stoichiometric TiN and Ti/TiN multilayer films are presented.     

Toward a Detector/Readout Architecture for the Background-Limited Far-IR/Submm Spectrograph (BLISS)

We have built and tested 32-element linear arrays of absorber-coupled transition-edge sensors (TESs) read out with a time-division SQUID multiplexer. This detector/readout architecture is designed for the background-limited far-IR/submm spectrograph (BLISS) which is a broadband (35–433  \(\upmu \) m), grating spectrometer consisting of six wavebands each with a modest resolution of R \(\sim \) 700. Since BLISS requires the effective noise equivalent power (NEP) of the TESs to equal 1  \(\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) , our detectors consist of very long (1–2 mm), narrow (0.4 \(\upmu \) m), and thin (0.25 \(\upmu \) m) Si \(_{x}\) N \(_{y}\) support beams that reduce the thermal conductance G between the substrate and the optical absorber. The thermistors of our lowest noise TESs consist of iridium with \(T_{c}=130\) mK. We have measured the electrical properties of arrays of these Ir TESs with various meander and straight support beams and absorber shapes and found that G is \(\sim \) 30 fW/K (meander) and \(\sim \) 110 fW/K (straight), the electrical NEP is 2–3  \(\times \)  10 \(^{-19}\) W/Hz \(^{1/2}\) (meander and straight), and the response time \(\tau \) is 10–30 ms (meander) and 2–5 ms (straight). To reduce spurious or “dark” power from heating the arrays, we mounted the arrays into light-tight niobium boxes and added custom L/R and L/C low-pass chip filters into these boxes to intercept dark power from the bias and readout circuit. We found the average dark power equals 1.3 and 4.6 fW for the boxes with L/R and L/C chip filters, respectively. We have built arrays with \(T_{c}= 70\)  mK using molybdenum/copper bilayers and are working to lower the dark power by an order of magnitude so we can demonstrate NEP \(~=~1~\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) with these arrays. PACS numbers: 85.25.Pb; 95.85.Gn; 95.85.Fm; 63.22. \(+\) m     

Study on the Difference Between the Triple-Point Temperatures of ^{20}Ne and ^{22}Ne Using Sealed Cells

At the National Metrology Institute of Japan (NMIJ), the triple points of \(^{20}\) Ne and \(^{22}\) Ne were realized using modular sealed cells, manufactured by the Istituto Nazionale di Ricerca Metrologica (INRiM) in Italy to measure the difference of the triple-point temperatures of \(^{20}\) Ne and \(^{22}\) Ne. Standard platinum resistance thermometers (SPRTs) were used that were calibrated by NMIJ on the International Temperature Scale of 1990 (ITS-90). In previous reports, sealed cells of \(^{20}\) Ne and \(^{22}\) Ne were mounted one at a time in a cryostat and their triple points were realized in separate cool-downs (the single-cell measurement). In this study, first, the triple point was realized using the single-cell measurement for \(^{20}\) Ne and \(^{22}\) Ne cells. Second, the \(^{20}\) Ne and \(^{22}\) Ne cells were mounted together on the same copper block and their triple points were realized subsequently one after the other in the same cool-down of the cryostat (the double-cell measurement). The melting curves observed by the single-cell and the double-cell measurements were almost identical for each cell. The difference of the triple-point temperatures between the two cells, \(^{22}T -^{20}\!T\) , was estimated, not only using the subrange of SPRTs defined in the ITS-90 from 13.8033 K to 273.16 K (subrange 1) but also that defined from 24.5561 K to 273.16 K (subrange 2). The difference in \((^{22}T-^{20}\!\!T)\) between the subranges 1 and 2 is within 0.06 mK, which is caused by the subrange inconsistency in the ITS-90. The standard uncertainty in \((^{22}T-^{20}\!T)\) due to the subrange inconsistency is estimated to be 0.017 mK. After correction for the effects of impurities and other isotopes in the \(^{20}\) Ne and \(^{22}\) Ne cells, the difference in the triple-point temperatures between pure \(^{20}\) Ne and pure \(^{22}\) Ne is estimated to be 0.146 64 (5) K on subrange 1, which is consistent within the uncertainty with the former studies. When \(^{22}T-^{20}\!T\) for pure \(^{20}\) Ne and pure \(^{22}\) Ne is estimated on subrange 2, \(^{22}T-^{20}\!\!T\) becomes 0.146 60 (5), which agrees very well with the former reports of INRiM evaluating \(^{22}T-^{20}\!T\) on subrange 2.     

Containerless Measurements of Density and Viscosity for a Cu_{48}Zr_{52} Liquid

The densities of solid and liquid Cu \(_{48}\) Zr \(_{52}\) and the viscosity of the liquid were measured in a containerless electrostatic levitation system using optical techniques. The measured density of the liquid at the liquidus temperature (1223 K) is (7.02 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) and the density of the solid extrapolated to that temperature is (7.15 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) . The thermal expansion coefficients measured at 1223 K are (6.4 \(\pm \) 0.1) \(\,\times \,10^{-5}\) K \(^{-1}\) in the liquid phase and (3.5 \(\pm \) 0.3) \(\,\times \,10^{-5}\) K \(^{-1}\) in the solid phase. The viscosity of the liquid, measured with the oscillating drop technique, is of the form \(A\exp \left[ \left( {{E}_{0}}+{{E}_{1}}\left( 1/T-1/{{T}_{0}} \right) \right) \times \left( 1/T-1/{{T}_{0}} \right) \right] \) , where \({{T}_{0}}=1223\) K, \(A= (0.0254 \pm 0.0004)\) Pa \(\cdot \) s, \({{E}_{0}}\) =  (8.43 \(\pm \) 0.26) \(\,\times \,10^3\) K and \({{E}_{1}}\) =  (1.7 \(\pm \) 0.2) \(\,\times 10^7\) K \(^{2}\) .     

Four-Channel Current-Biased Kinetic Inductance Detectors Using MgB_2 Nanowires for Sensing Pulsed Laser Irradiation

We recently proposed the idea of a novel sort of superconducting detector, i.e., a current-biased kinetic inductance detector (CB-KID). This detector is different from a current-biased transition edge detector studied previously, and is able to sense a change in kinetic inductance \(L_k\) given by \(L_{k} = \Lambda _{k}l/S = m_{s}l/n_{s}{q_{s}}^{2}S\) ( \(\Lambda _{k}\) ; kinetic inductivity, \(m_s\) ; mass of Cooper pair, \(n_s\) ; density of Cooper pairs, \(q_s\) ; charge of Cooper pair, \(l\) ; length of device, \(S\) ; cross sectional area) under a constant dc bias current \(I_b\) . In the present work, we first extend this idea to construct a multi-channel CB-KIDs array made of 200-nm-thick MgB \(_2\) thin-film meanderline with 3- \(\upmu \) m thin wire. We succeeded in observing clear signals for imaging from the four-channel CB-KIDs at 4 K by irradiating focused pulsed laser. A scanning laser spot can be achieved by an XYZ piezo-driven stage and an optical fiber with an aspheric focused lens. We can see typical signals from all 4 channels at 4 K, and obtain the positional dependence of the signal as the contour in XY plane. Our CB-KIDs can be used as neutron detectors by utilizing energy released from a nuclear reaction between \(^{10}\) B and cold neutron.     

High-Frequency Shear Viscosity of Low-Viscosity Liquids

A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times \(\tau _{\eta }\) of about 0.3 ns for \(n\) -pentadecane and \(n\) -hexadecane at 25  \(^{\circ }\) C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which \(\tau _{\eta }\) values between 0.3 ns ( \(n\) -hexanol) and 1.5 ns ( \(n\) -dodecanol) have been found at 25  \(^{\circ }\) C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity \(\eta _\mathrm{bg}\) of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in \(\eta _\mathrm{bg}\) appear also in the shear-viscosity spectra with, for example, \(\tau _{\eta }\,\approx \) 2 ns for the critical triethylamine–water binary mixture at temperatures between 10  \(^{\circ }\) C and 18  \(^{\circ }\) C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.     

Fabrication of Nb/Al Superconducting Tunnel Junction Using Ozone Gas

An ozone (O \(_{3})\) oxidation process was introduced for Nb/Al-based superconducting tunnel junctions (STJs) in order to form defect-free tunnel barriers at high critical current and to improve the energy resolution ( \(\Delta E\) ) for X-rays. The dependence of critical current ( \(J_\mathrm{C})\) and leak current ( \(I_\mathrm{leak})\) on the O \(_{3}\) exposure was measured to optimize the oxidation condition. The 50-square- \(\upmu \) m STJs produced by the O \(_{3}\) oxidation process exhibited an extremely small \(I_\mathrm{leak}\) of less than 50 pA. As expected, the lower or shorter the O \(_{3}\) exposure, the higher \(J_\mathrm{C}\) and the smaller the normal resistance ( \(R_\mathrm{N})\) . However, the maximum \(J_\mathrm{C}\) was 8 A/cm \(^{2}\) at an O \(_{3}\) exposure of 0.72 Pa min, which is much smaller than those of STJs with the conventional O \(_{2}\) oxidation process. It is expected that the high \(J_\mathrm{C}\) of 1,000 A/cm \(^{2}\) , at which a 9-eV-energy resolution for 277 eV photons is predicted, can be reached by an O \(_{3}\) exposure of 3.5 \(\times \) 10 \(^{-4}\) Pa min.     

Exploring Solute–Solvent Interactions of \alpha -Amino Acids in Aqueous [\mathrm{EPyBF}_{4}] Arrangements by Volumetric,Viscometric, Refractometric,and Acoustic Approach

Qualitative and quantitative analysis of molecular interaction prevailing in glycine, l-alanine, l-valine, and aqueous solution of ionic liquid (IL) [1-ethylpyridinium tetrafluoroborate ( \(\mathrm{EPyBF}_{4})\) ] have been investigated by thermophysical properties. The apparent molar volume ( \(\phi _{V}\) ), viscosity \(B\) -coefficient, molal refraction ( \(R_{\mathrm{M}}\) ), and adiabatic compressibility ( \(\phi _{ K} )\) of glycine, l-alanine, and l-valine have been studied in 0.001 mol \({\cdot }\, \mathrm{dm}^{-3}\) , 0.003 mol \({\cdot }\, \mathrm{dm}^{-3}\) , and 0.005 mol  \({\cdot } \,\mathrm{dm}^{-3}\) aqueous 1-ethylpyridinium tetrafluoroborate [ \(\mathrm{EPyBF}_{4}\) ] solutions at 298.15 K from the values of densities \((\rho )\) , viscosities ( \(\eta \) ), refractive index ( \(n_{\mathrm{D}})\) , and speed of sound \((u)\) , respectively. The extent of interaction, i.e., the solute–solvent interaction is expressed in terms of the limiting apparent molar volume ( \(\phi _{V}^0 )\) , viscosity \(B\) -coefficient, and limiting apparent molar adiabatic compressibility ( \(\phi _{K}^0)\) . The limiting apparent molar volumes ( \(\phi _{V}^0 )\) , experimental slopes ( \(S_{V}^*)\) derived from the Masson equation, and viscosity \(A\) - and \(B\) -coefficients using the Jones–Dole equation have been interpreted in terms of ion–ion and ion–solvent interactions, respectively. Molal refractions ( \(R_{\mathrm{M}})\) have been calculated with the help of the Lorentz–Lorenz equation. The role of the solvent (aqueous IL solution) and the contribution of solute–solute and solute–solvent interactions to the solution complexes have also been analyzed through the derived properties.     

Development of Multilayer Readout Wiring TES Calorimeter for Future X-ray Missions

We have fabricated multilayer readout wiring transition edge sensors (TES), which enable us to realize both large effective area and high-energy resolution for future X-ray astrophysical missions, such as diffuse intergalactic oxygen surveyor. By sandwiching a SiO \(_2\) insulation layer between Al superconducting signal and return lines, self/mutual inductances and self fielding of bias leads are expected to be reduced. We fabricated \(4\times 4\) and \(20\times 20\) TES array on the multilayer wiring and tested their performance. Under the low temperature condition, several pixels in the TES array showed sharp superconducting transitions at around \(\sim \) 300 mK. We also succeeded in detecting X-ray signals from the \(4\times 4\) TES, contrary to the previous results of \(20\times 20\) TES. We further investigated the reasons for the differences between the \(4\times 4\) TES and the \(20\times 20\) TES, and present future plans for improving the multilayer TES array fabrication.     

Comparing Transition-Edge Sensor Response Times in a Modified Contact Scheme with Different Support Beams

We present measurements of the thermal conductance, G, and effective time constants, \(\tau \) , of three transition-edge sensors (TESs) populated in arrays operated from 80–87 mK with T \(_\mathrm{C}\)   \(\sim \)  120 mK. Our TES arrays include several variations of thermal architecture enabling determination of the architecture that demonstrates the minimum noise equivalent power, the lowest \(\tau \) , and the trade-offs among designs. The three TESs we report here have identical Mo/Cu bilayer thermistors and wiring structures, while the thermal architectures are: (1) a TES with straight support beams of 1 mm length, (2) a TES with meander support beams of total length 2 mm and with two phonon-filter blocks per beam, and (3) a TES with meander support beams of total length 2 mm and with six phonon-filter blocks per beam. Our wiring scheme aims to lower the thermistor normal state resistance R \(_{N}\) and increase the sharpness of the transition \(\alpha =\)  dlogR/dlogT at the transition temperature T \(_\mathrm{C}\) . We find an upper limit of \(\alpha \) given by ( \(25\pm 10\) ), and G values of 200 fW/K for (1), 15 fW/K for (2), and 10 fW/K for (3). The value of \(\alpha \) can be improved by slightly increasing the length of our thermistors.     

Study on Optical Filter Heating in Background Limited Detector Experiments

Cryogenic test setups with controlled stray light environments capable of reaching ultra-low radiative background levels are required to test far infrared (FIR) and submillimeter (sub-mm) wave radiation detectors for future space based observatories. In recent experiments (Nature Commun 5:3130, 2014), in which 1.54 THz radiation was coupled onto an antenna-coupled kinetic inductance detector (KID), we found a higher than expected optical loading. We show that this can be explained by assuming heating of the metal mesh IR filters and re-radiation onto the KID. Note that the total power from the cryogenic black body source used in the experiments (at T = \(3\) – \(25\) K) is much larger than the power inside the \(1.5\) – \(1.6\) THz band we use to calibrate our detector. The out-of-band radiation can have up to 5 orders of magnitude more power than inside the \(1.5\) – \(1.6\)  THz band of interest. A strategy to mitigate the filter heating problem is presented, and when it is implemented, the validated upper limit for stray light at the detector level is down to few aW.     

Ternary codes from some reflexive uniform subset graphs

We examine the ternary codes \(C_3(A_i+I)\) from matrices \(A_i+I\) where \(A_i\) is an adjacency matrix of a uniform subset graph \(\Gamma (n,3,i)\) of \(3\) -subsets of a set of size \(n\) with adjacency defined by subsets meeting in \(i\) elements of \(\Omega \) , where \(0 \le i \le 2\) . Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the \(C_3(A_i+I)\) are also examined.     

First- and Second-Order Phase Transition in Parallel Triple Quantum Dots: The Roles of Symmetric and Asymmetric Hopping

By means of the numerical renormalization group method, I study the quantum phase transition (QPT) and the electronic transport in parallel triple quantum dot system with symmetric and/or asymmetric hopping. For symmetric hopping \(t_{1} = t_{2}\) and zero magnetic field \(B = 0\) , I find a first order transition between spin quadruplet and doublet as \(t_{1}\) ( \(t_{2}\) ) increases. With increasing \(B\) , a second order QPT between \(S_{z} = 1/2\) of the doublet and \(S_{z} = 3/2\) of the quadruplet is observed. For asymmetric hopping \(t_{1} \ne t_{2}\) , the QPT depends closely on the other hopping. For fixed \(t_{1} < \varGamma \) , where \(\varGamma \) is the hybridization function between the dots and the leads, a first order transition is observed as \(t_{2}\) increases, while for \(t_{1} \ge \varGamma \) , a crossover occurs. In the presence of \(B\) , the transition between \(S_{z} = 1/2\) and \(S_{z} = 3/2\) is a first order QPT for \(t_{1} < \varGamma \) , while a second order for \(t_{1} \ge \varGamma \) .     

An algorithm for computing the error sequence of p^{n}-periodic binary sequences

For binary sequences with period \(p^{n}\) , where \(p\) is an odd prime and 2 is a primitive root modulo \(p^{2}\) , we present an algorithm which computes the minimum number \(k\) so that the \(k\) -error linear complexity is not greater than a given constant \(c\) . An associated error sequence which gives the \(k\) -error linear complexity is also obtained.     

A New Functional Form for Equations of State for Some Weakly Associating Fluids

A new functional form for equations of state for polar and weakly associating fluids was developed. It was established with a simultaneous optimization algorithm developed previously. As a result, equations of state in terms of the Helmholtz energy as a function of temperature and density were developed for hydrogen chloride (HCl) valid within \(T =\) (155–330) K and pressures up to \(p = 20\) MPa, diethyl ether (DEE) valid within \(T =\) (270–500) K and pressures up to \(p = 40\) MPa, and methyl chloride (R40) valid within \(T =\) (230–630) K and pressures up to \(p =\) 100 MPa. Those equations can be used for the calculation of all thermodynamic properties, including density, internal energy, enthalpy, heat capacity, speed of sound, saturation properties, etc.     

Some results on the differential functions over finite fields

Let \(g\) be a function over \(\mathbb {F}_q\) . If there exist a function \(f\) and \(a\in \mathbb {F}_q^*\) such that \(g(x)=f(x+a)-f(x)\) , then we call \(g\) a differential function and call \(f\) a differential-inverse of \(g\) . We present two criteria to decide whether a given \(g\) is a differential function. The set of the degrees of all differential functions over \({\mathbb {F}}_q\) is determined. Then we give a lower bound and an upper bound on the number of differential functions over \({\mathbb {F}}_q\) . Besides, we show how to construct differential inverses of a given differential function. At last, some applications of our results are introduced.