Thomas Fincke and trigonometry

Thomas Fincke (January 6th, 1561 - April 24th, 1650), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughtout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be ,,abreast of the mathematics of his time".     

An All‐Solution‐Based Hybrid CMOS‐Like Quantum Dot/Carbon Nanotube Inverter

The development of low‐cost, flexible electronic devices is subordinated to the advancement in solution‐based and low‐temperature‐processable semiconducting materials, such as colloidal quantum dots (QDs) and single‐walled carbon nanotubes (SWCNTs). Here, excellent compatibility of QDs and SWCNTs as a complementary pair of semiconducting materials for fabrication of high‐performance complementary metal‐oxide‐semiconductor (CMOS)‐like inverters is demonstrated. The n‐type field effect transistors (FETs) based on I^? capped PbS QDs (V _th = 0.2 V, on/off = 10⁵, S _S‐th = 114 mV dec^?1, µ _e = 0.22 cm² V^?1 s^?1) and the p‐type FETs with tailored parameters based on low‐density random network of SWCNTs (V _th = ?0.2 V, on/off > 10⁵, S _S‐th = 63 mV dec^?1, µ _h = 0.04 cm² V^?1 s^?1) are integrated on the same substrate in order to obtain high‐performance hybrid inverters. The inverters operate in the sub‐1 V range (0.9 V) and have high gain (76 V/V), large maximum‐equal‐criteria noise margins (80%), and peak power consumption of 3 nW, in combination with low hysteresis (10 mV).     

Ordered oxygen deficient ‘112’ perovskites,LnBaCo<Subscript>2</Subscript>O<Subscript>5·50+<Emphasis Type="Italic">δ</Emphasis></Subscript>: complex magnetism and transport properties

The ordered oxygen deficient ‘112’ perovskites, LnBaCo₂O_5·50+δ (Ln = lanthanide or Y), exhibit a very flexible structure which can either uptake (δ > 0) or release oxygen (δ < 0) depending on the experimental conditions of synthesis and on the size of the lanthanide. These compounds exhibit remarkably complex magnetic transitions, metal-insulator transition and exceptionally high magnetoresistance. We show herein that their physics is mainly dominated by three different ferromagnetic states, depending on the cobalt valency: FM1 for δ = 0 (Co³⁺), FM2 for δ < 0 (Co²⁺/Co³⁺) and FM3 for δ > 0 (Co³⁺/Co⁴⁺). The competition between ferromagnetism and antiferromagnetism in these phases and the various transitions are discussed taking into consideration the spin state of cobalt, the issue of phase separation and the effect of cobalt coordination and disproportionation. In honour of Prof. C N R Rao on his 75th birthday     

Study of Screening Dependence Superconducting State Parameters of Cu<Subscript><Emphasis Type="Italic">C</Emphasis></Subscript>Zr<Subscript>100−<Emphasis Type="Italic">C</Emphasis></Subscript> Binary Metallic Glasses by a Pseudopotential

The screening dependence theoretical investigations of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ ^*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of ten binary Cu _C Zr_100−C (C=25, 30, 33, 35, 40, 45, 50, 55, 57 and 60) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F), and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron–phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ ^*, isotope effect exponent α and effective interaction strength N _O V show weak dependences on the local field correction functions. The values of T _C obtained from the H-local field correction function are in qualitative agreement with available theoretical or experimental data and show almost linear nature with the concentration C of Cu element. A linear T _C equation is proposed by fitting the present outcomes for the H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.     

Ion-selective properties of metastable (VO)<Subscript>0.09</Subscript>V<Subscript>0.18</Subscript>Mo<Subscript>0.82</Subscript>O<Subscript>3</Subscript> · 0.54H<Subscript>2</Subscript>O

This paper describes a thin-film solid electrode with an ion-sensitive membrane based on the mixed oxide (VO)_0.09V_0.18Mo_0.82O₃ · 0.54H₂O. The electrode is selective for tetravalent vanadium in the concentration range 3 ≤ pC _V ⁴⁺ ≤ 5 and acidity range 4.5 ≤ pH ≤ 6, with a slope close to the theoretical value. In the range 1 ≤ pH < 5, the electrode responds to changes in hydrogen ion concentration, with a slope of 50 ± 2 mV/pH. Its alkali-metal-ion response shows up in the range 1 ≤ pC _M ⁺ ≤ 4 for pH ≥ 6. We examine the effect of the Li⁺, K⁺, Na⁺, Cs⁺, Rb⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Co²⁺, Ni²⁺, Mn²⁺, Al³⁺, Cr³⁺, and VO₂⁺ ions on the potential of the electrode and determine its selectivity coefficients for these cations.     

Magnetic and Superconducting Properties of Doped and Undoped Double Perovskite Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript>

We report here SQUID (magnetization) measurements, along with supporting specific heat, Raman, SEM (scanning electron microscope), EDX (energy dispersive X-ray) and XRD (X-ray diffraction) measurements, on Cu-doped and undoped double perovskite Sr₂²⁺Y³⁺Ru⁵⁺O₆^2-\mathrm{Sr}_{2}^{2+}\mathrm{Y}^{3+}\mathrm{Ru}^{5+}\mathrm{O}_{6}^{2-} (abbreviated as SrY2116) system grown as single crystal using high-temperature solution growth technique. These measurements show the undoped system to be a nonmetallic (insulating) spin glass (SG) and the ∼5–30% Cu-doped (i.e. Cu-concentration/(Cu + Ru-concentration) ∼5–30%) system to be a spin glass superconductor (SGSC) with T _c (critical temperature) ∼28–31 K and superconducting volume fraction, f _sc∼2.2–9%. To mention, similar measurements done on undoped and Cu-doped BaY2116 and BaPr2116 systems show for them the same (SG, SGSC) behaviors. However they show a decrease in T _c and f _sc when diamagnetic Y³⁺ ions are replaced by Pr³⁺ spins, presumably due to enhanced internal pair breaking, and also decreased Cu–O–Cu overlap, owing to Pr³⁺ presence; these phenomena are known to exist in the Pr123 compound, PrBa₂Cu₃O_7−δ (δ∼0), due to ∼10% of Pr³⁺ ions having tendency to occupy Ba²⁺ sites. Measurements done on undoped and Cu-doped SrHo2116 show similar SG and SGSC properties. Further, the undoped and Cu-doped SrY2116 crystals grown by hydrothermal growth technique (i.e., grown using lower temperature and high pressure) show same behaviors. From these investigations it can be said that the undoped Ru-double perovskites (A₂BB′O₆, B′=Ru) are SG systems and that Cu-doped Ru-double perovskites (A₂BB′O _δ , δ∼6, B′=Ru_1−x Cu _x , 0<x≲0.3) are SG superconductors (SGSCs). Results are discussed.     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

Emissive characteristics of mesa-stripe lasers (λ=3.0–3.6 μm) made from InGaAsSb/InAsSbP double heterostructures

The directional patterns, current-voltage characteristics, and spectral characteristics of mesastripe lasers with InGaAsSb active layers, emitting at λ=3.0–3.6 μm (77 K) and having threshold currents ≥15 mA (j _th≥200 A/cm²), are investigated. The maximum output power is 1.4 mW (λ∼3.3 μm), the differential quantum efficiency ∼3%(τ=5–30 μs, f=500 Hz) for lasing in a longitudinal mode with beam divergences ΔΘ∥∼15° and ΔΘ ⊥ ∼30°. The relationship of the differential quantum efficiency to the order of the spatial mode of the lasing is demonstrated. A single-mode, current-tunable (−30 cm⁻¹/A) laser is used to measure the transmission of methane in the region of the ν ₃ absorption band. Pis’ma Zh. Tekh. Fiz. 24, 40–45 (June 26, 1998)     

Luminescence of europium-doped BaO-Bi<Subscript>2</Subscript>O<Subscript>3</Subscript>-B<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

We have prepared europium-doped BaO-Bi2O₃-B2O₃ glasses and investigated the doping effect on the main physicochemical properties and local structure of the glasses. Using Judd-Ofelt analysis, we calculated intensity parameters (Ω₂, Ω₄, and Ω₆), spontaneous emission probabilities, the radiative lifetime, luminescence branching factors, the quantum yield of luminescence, and the stimulated emission cross sections for ⁵ D ₀ → ⁷ F _J transitions.     

Synthesis and characterization of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–ZrO<Subscript>2</Subscript> nanocomposite powder by sucrose process

Nanocrystalline alumina–zirconia powders were prepared by a modified chemical route using sucrose, polyvinyl alcohol (PVA) and metal nitrates followed by a post calcination process. The process involved dehydration of Al³⁺–Zr⁴⁺ ions-sucrose–PVA solution to a highly viscous liquid which on decomposition process produced a black precursor material. The obtained precursor were then calcined at various temperatures: 1,050, 1,100, 1,150, 1,200 and 1,250 °C for different soaking times (1, 2, 4 h) in air. The formation of a nanocomposite composed of α-alumina (~20 nm) and tetragonal (t) zirconia (~19 nm) crystallites were confirmed for the sample calcined at 1,200 °C for 2 h, based on our XRD and TEM results. However, for the samples calcined below 1,150 °C the composite formed were composed of metastable alumina (γ, δ, θ) as well as t-zirconia phases. Interestingly, the zirconia phase retained its tetragonal structure for all the samples calcined above 1,050 °C. This is possibly related to the “size effect” and reduction of surface enthalpy of the zirconia crystallites surrounded by Al³⁺ cations.     

Long binary narrow-sense BCH codes are normal

Let C be the binary narrow-sense BCH code of length n = (2 ^m − l)/h, where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2^m ≥ 4(2th)^{4t + 2}, and in the primitive case h = 1 if m ≥ m ₀ where the constant m ₀ depends only on t.     

Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Superconducting State Parameters of MgB<Subscript>2</Subscript>: <Emphasis Type="Italic">Ab Initio</Emphasis> Study

Harrison’s first principle pseudopotential (HFPP) technique in conjunction with BCS theory and McMillan’s formalism has been used for the investigation of superconducting state parameters viz., Coulomb pseudopotential μ ^∗, electron–phonon coupling strength λ, SC transition temperature T _C , interaction strength N ₀ V, semi band gap Δ, energy or mass renormalization parameter Z ₀ and isotope effect exponent δ. The ground state properties of MgB₂ have also been calculated employing full-potential linearized augmented plane wave (FLAPW) method. This enables us to estimate the equilibrium values of bulk modulus and its pressure derivative through optimization of the crystal structure of the system. We have also described the total density of state (DOS) and the partial DOS (PDOS) around the Fermi energy.     

Effect of low level substitution of Sr–Ba on transport and magnetic behaviour of La<Subscript>0·67</Subscript>Ca<Subscript>0·33</Subscript>MnO<Subscript>3</Subscript>

In this paper we report the investigation of transition metal oxide compound, La_0·67Ca_0·25Sr_0·04Ba_0·04MnO₃ (LCSBMO), along with La_0·67Ca_0·33MnO₃ (LCMO), synthesized by sol–gel route under identical conditions. The effect of simultaneous low level substitution of large size ions such as Sr²⁺ and Ba^2 + for Ca^2 + ions on the electronic transport and magnetic susceptibility properties are analysed and compared apart from microstructure and lattice parameters. The temperature dependent electrical transport of the polycrystalline pellets of LCSBMO and LCMO when obeying the well studied law, r = r₀ + r₂   T²\rho = \rho_{0} + \rho_{2} \;T^{2} for T < T _MI , is observed to differ by more than 50% from the values of ρ ₀ and ρ ₂, with the former compound showing enhanced electrical conductivity than the latter. Similarly in fitting the adiabatic small polaron model for resistivity data of both the samples for T > T _MI , the polaron activation energy is found to differ by about 11%. In addition, the temperature dependent a.c. magnetic susceptibility study of the compounds shows a shift of about 6% in the paramagnetic to ferromagnetic transition temperature (285 K for LCSBMO and 270 K for LCMO).     

Li-storage and cycling properties of spinel,CdFe<Subscript>2</Subscript>O<Subscript>4</Subscript>, as an anode for lithium ion batteries

Cadmium ferrite, CdFe₂O₄, is synthesized by urea combustion method followed by calcination at 900°C and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HR-TEM) and selected area electron diffraction (SAED) techniques. The Li-storage and cycling behaviour are examined by galvanostatic cycling, cyclic voltammetry (CV) and impedance spectroscopy in the voltage range, 0·005–3·0 V vs Li at room temperature. CdFe₂O₄ shows a first cycle reversible capacity of 870 (± 10) mAhg⁻¹ at 0·07C-rate, but the capacity degrades at 4 mAhg⁻¹ per cycle and retains only 680 (± 10) mAhg⁻¹ after 50 cycles. Heat-treated electrode of CdFe₂O₄ (300°C; 12 h, Ar) shows a significantly improved cycling performance under the above cycling conditions and a stable capacity of 810 (± 10) mAhg⁻¹ corresponding to 8·7 moles of Li per mole of CdFe₂O₄ (vs theoretical, 9·0 moles of Li) is maintained up to 60 cycles, with a coulombic efficiency, 96–98%. Rate capability of heat-treated CdFe₂O₄ is also good: reversible capacities of 650 (± 10) and 450 (± 10) mAhg⁻¹ at 0·5 C and 1·4 C (1 C = 840 mAg⁻¹) are observed, respectively. The reasons for the improved cycling performance are discussed. From the CV data in 2–15 cycles, the average discharge potential is measured to be ∼0·9 V, whereas the charge potential is ∼2·1 V. Based on the galvanostatic and CV data, ex situ-XRD, -TEM and -SAED studies, a reaction mechanism is proposed. The impedance parameters as a function of voltage during the 1st cycle have been evaluated and interpreted. Dedicated to Prof. C N R Rao on his 75th birthday, and his contributions to science for the past 56 years     

Formation and properties of SnO–MgO–P<Subscript>2</Subscript>O<Subscript>5</Subscript> glasses

A new glass system SnO–MgO–P₂O₅ with low viscosity has been developed by a melt-quenching method. Formation, thermal properties, and chemical durability of these glasses have been investigated. For a constant P₂O₅ concentration, the glass formation ability is enhanced with the increasing Sn/(Sn + Mg) ratio. The glasses exhibit low glass transition temperature (T _g = 270–400 °C), low dilatometric softening temperature (T _DS = 290–420 °C), and high thermal expansion coefficient (CTE = 110–160 × 10⁻⁷ K⁻¹). With the increasing Sn/(Sn + Mg) ratio, T _g and T _DS decrease, and CTE increases. When Sn/(Sn + Mg) ratio is varied, the relationship between chemical durability and thermal properties of the present glasses is not consistent with what expected in general cases. It is noted that the glasses with 32–32.5 mol% P₂O₅ exhibit excellent chemical durability and tunable T _g, T _DS, and CTE (by varying Sn/(Sn + Mg) ratio).     

Samuel Reyher und sein <Emphasis Type="Italic"> In Teutscher Sprache vorgestellter Euclides</Emphasis>

In 1665 in the city of Kiel there was founded a new university called Christiana Albertina or Alma mater Chiloniensis. It was the only one in the duchies of Schleswig and Holstein. One of the leading scientists of this academy was the mathematician Samuel Reyher (1635–1714) who didn’t teach mathematics only but also physics, and astronomy, and engineering, and jurisprudence. He was the author of a comprehensive Historia iurium universalis (1711) and of an extraordinary work Mathesis Mosaica (1679). But he was best known for his In Teutscher Sprache vorgestellter Euclides (1697, 1699), one of the earliest translations of Euclid’s Elements into German. In this book Samuel Reyher tried to prove the euclidean 5th postulate (the postulate [axiom] of parallels) - believing that he was successful.     

Esperanza condicionada para probabilidades finitamente aditivas

Let (Ω, θ,J) be a finitely additive probabilistic space formed by any set Ω, an algebra of subsets θ and a finitely additive probabilityJ. In these conditions ifF belongs toV ¹ (Ω, θ,J) there existsf, element of the completion ofL ¹ (Ω, θ,J), such thatF(E)=∫ _E fdJ for allE of θ and conversely. This integral representation gives sense to the following result, which is the objetive of this paper, in terms of the, point function: If β is a subalgebra of θ, for everyF ofV ¹ (Ω, θ,J) there exists a unique element ofV ¹ (Ω, β,J) which we note down byE(F/gb), conditional expetation ofF given β. E(F/β) is characterized by (E(F/β),G)=(F, G) for every ofV ^∞(Ω,β, J). Aside from this, the mappingE(./β):V ¹ (Ω, θ,J)→V ¹ (Ω, β,J) is linear, positive, contractive, idempotent andE(J/β)=J. IfF is ofV ^p (Ω, θ,J),p>1,E(F/β) is ofV ^p (Ω, β,J).

     

The Activation Energy <Emphasis Type="Italic">U</Emphasis>(<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">H</Emphasis>) in Y-based Superconductors

Based on the Arrhenius equation, a method to calculate the activation energy from the resistance transition is proposed for high temperature superconductors. This method is applied to the Y-based superconductors. The activation energy is found to be U(T,H)∼(1−T/T _c )^4.8(H/H ₀)^−3.8 of YBCO crystal, and U(T,H)∼(1−T/T _c )^3.3(H/H ₀)^−2.2 of Er doped MTG YBCO crystal, respectively. With the obtained activation energy U(T,H), the lower part of the experimental curve ρ(T,H) and its derivative can be reproduced.