A comparison of the Schumacher with other functions for describing growth in pigs

This study was undertaken to introduce the Schumacher equation and compare it with established functions for describing growth in pigs. The relationship between live weight (LW) and cumulative feed intake was also investigated. A database was constructed from three independent trials in which LW, age and intake were measured from birth to 937 days. Three growth functions were used for analysis of growth versus age: Gompertz, Schumacher and Weibull; and the Richards and monomolecular equations were used for analysis of cumulative feed intake versus LW. The growth functions have different points of inflexion. Liveweight at inflexion is W_f/e for the Gompertz, where W_f is the final weight, W_f/e² for the Schumacher, and W_f − (W_f − W₀) exp[−(n − 1)/n] for the Weibull, where W₀ is initial body weight and n is a shape parameter. Meta-analysis of the data using mixed model and nonlinear regression procedures was conducted to identify the most appropriate growth function. Functions were compared using F-tests or Bayesian Information Criteria, which give a value based on best fit and number of parameters in the model. The three equations were fitted to five individual pig growth profiles and to the composite data. Although the Weibull had a lower residual mean square, it did not significantly improve the fit compared to the simpler models and appears to be over-parameterised. The results suggest that model selection should be based on the type and amount of data available for analysis. Residuals plot showed that Schumacher and Weibull better predict the initial growth phase, however, all models showed largest magnitude of residuals towards the end of the growth profile. The monomolecular equation was most appropriate for describing LW against cumulative feed intake and may be used to formulate diets based on the efficiency of conversion of feed to LW at various stages of the animal's life span.     

The effect of body size on food consumption, absorption efficiency, respiration, and ammonia excretion by the inland silverside, Menidia beryllina (Cope) (Osteichthyes: Atherinidae)

The inland silverside, Menidia beryllina (Cope), is an annual zooplanktivore that occurs in estuarine and freshwater habitats along the Atlantic and Gulf of Mexico coasts and drainages of the United States. Experiments were conducted at 25 ± 1°C to quantify the relationship between mean dry weight (W_D) and rates of energy gain from food consumption (C), and energy losses as a result of respiration (R) and ammonia excretion (E) during routine activity and feeding by groups of fish. The absorption efficiency of ingested food energy (A) was also quantified. Rates of C, E, and R increased with W_D by factors (b in the equation y = aW_D^b) equal to 0.462, 0.667, and 0.784, respectively. Mean (±SE) rates of energy loss during feeding were 1.6 ± 0.1 (R) and 3.4 ± 0.6 (E) times greater than those for unfed fish. Absorption efficiency was independent of W_D and estimated to be 89% of C. From these measurements, the surplus energy available for growth and activity (G) and growth efficiency (K₁) were estimated. Over the range in sizes of juveniles and adults (5–500 mg W_D), predicted G and K₁ values decreased from 7.42 to 0.20 J mg fish^?1 day^?1 and 63 to 21%, respectively. Measured and predicted bioenergetic parameters are discussed within an ecological context for a northern population of this species.     

Preliminary studies on the respiratory energy loss of a spider,Lycosa pseudoannulata

To elucidate the basic food requirement of spiders, the important polyphagous predators of rice-plant insect pests, an attempt was made to measure the respiratory energy loss of fasting spiders, Lycosa pseudoannulata. Relationship between fresh (y) and dry (x) weights of spiders inhabiting the bottom layer of the rice-plant community was represented by the following allometric equation:y=0.428x^0.872. The carbon dioxide production by previously fed and unfed females under the dark at 29°C 100% R. H. was measured by a titration technique. The relationship between fresh body weight and CO₂ production by unfed animals could be represented by the equation M=aW^b, M being the CO₂ output per individual per day and W the fresh body weight. The constant b, which determines the slope of curve, was 0.808. Respiration of the adult female with 100 mg fresh weight was 1.155±0.250 mg CO₂/100 g fresh weight/day or 48.69 mg CO₂/g dry weight/day. This value corresponds to 35.81 cal/g fresh weight/day or 150.94 cal/g dry weight/day. Supposing the calorific content of spiders to be 5820 cal/g dry weight, rate of the respiratory energy loss to total energy of the body was estimated to be 2.60%. This rate did not strongly contradict with the loss of fresh body weight before and after the measurement. The metabolic rate showed remarkable fluctuation with changing food supply. The CO₂ production of starved individuals decreased to 83.63±16.34% as compared with individuals which were fed before the measurement.     

Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions

Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ _R θ(x ₁,x ₂,t) dx ₁ dx ₂ of a biological species with an area-density distribution function θ=θ(x ₁,x ₂,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇²θ +fθ −gθ ⁿ⁺¹ whereD (>0),n (>0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(_{x 1},x ₂, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn>1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ _R θ(x ₁,x ₂, 0)² dx ₁ dx ₂ sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.     

Equilibria in N-heterocyclic complexes. Part 45. Ligand electron densities in coordinated pyridine

Results of INDO calculations on the species pyridine (py), (pyH)⁺, [py-CH₃]⁺, [Fe(NH₃)_x(py)_6−x]²⁺, [Fe(NH₃)₅(py)]³⁺, [Fe(CN)₅(py)]³⁻, and [Co(CN)₅(py)]²⁻ are presented and discussed, comparing quaternization and coordination.     

Relationship between specific leaf area of aCryptomeria japonica foliage shoot segment and its diameter

Dependency of specific leaf area (SLA) on shoot diameter (x) was studied forCryptomeria japonica foliage shoot segments about 5 cm in length taken from 18 branches at different height levels on 3 trees in August 1987. The leaf area of a shoot segment (S) was defined as half the sum of the needle area (s) estimated by the allometric relationship betweens and needle length. The dry weight of woody tissue (W _w) and needles (W _n) of a segment and itsS were divided by the segment length (L) to give linear densities asW _w/L,W _n/L andS/L, respectively. The densities were related tox by power-form equations.S/L values tended to be constant around 1.2 [cm² cm⁻¹] within the discussed range ofx, whileW _w/L andW _n/L values clearly increased withx. The approximately reciprocal relationship between average needle area (s) and linear density of the number of needles supported the fact thatS/L values were roughly constant regardless ofx.SLA andSNA were defined asS/(W _w+W _n) andS/W _n, respectively. TheSLA-x relationship expected from the average value ofS/L and theW _w/L-x and theW _n/L-x relationships was well fitted to the observed decrease inSLA with increasingx. SNA also decreased asx increased. Variations inSLA andSNA among the shoot segments with similarx were not systematically related to their height levels. An empirical equation with a maximum value ofx (Xmax) was also proposed in order to formulate theSLA-x relationship.     

Modeling population dynamics of yeast-like symbionts (Ascomycota: Pyrenomycetes: Clavicipitaceae) of the planthopper <Emphasis Type="Italic">Delphacodes kuscheli</Emphasis> (Hemiptera: Delphacidae)

Delphacodes kuscheli establish mutualistic relationship with yeast-like symbionts (YLS) that live in the fat body and are necessary for host survival and reproduction. We estimated for a host of age t, its body weight, W_(t), and the number of YLS per host, YLS_(t). The host body weight was calculated as: W_(t)?=?Lm/[1+ e ^(d–kt)], (Lm?=?the maximum observed weight, and d and k are constants), and the fat body was considered a fixed proportion of W_(t). We calculated the number of YLS per unit host body mass: α_(t)?=?YLS_(t)/W_(t). We also calculated the number of YLS per host, cYLS_(t), and analyzed the pattern of variation in both sexes adapting the expression of the logistic model: cYLS_(t)?=?KN_oe^rt/K+(e^rt -1)N_o, (N_o?=?initial number of YLS, r?=?intrinsic per capita rate of natural increase, and K?=?variable carrying capacity). In females the carrying capacity varied according to a constant proportion of the host’s weight: K_(t)?=?αW_(t). In males α_(t) was considered a decreasing function of the host age: K_(t)?=?α_(t)W_(t). The coefficients No, α, and r were subjected to parameterization. We found that the patterns of W_(t) and YLS_(t) of D. kuscheli were similar to other planthoppers. In females YLS increased up to the adult stage and then remained almost constant, varying similarly to individual weight. In males YLS increased up to the 5th instar nymph as the individual weight did, but the number of YLS decreased in the adult stage and the correlation was not so good. The calculated number of YLS per host matches reasonably well with the number estimated experimentally both in females and males. This is the first study that quantified and modeled the dynamics of YLS endosymbionts in a Neotropical planthopper pest. The models will be used in future studies for better understand the experimental reduction of YLS in young nymphal stages.     

Energetics of Shortening Muscles in Twitches and Tetanic Contractions : II. Force-Determined Shortening Heat

The extra heat liberation accompanying muscular shortening, the force-determined shortening heat, is defined as the difference between the heat produced when shortening occurs and that produced in an isometric contraction developing the same amount of force and performing the same amount of internal work. Based on this definition, the initial energy production in twitches and tetanic contractions (E) is given by E = A + f (P, t) + α_Fx + W, where A is the activation heat, f(P, t), the tension-related heat (a heat production associated with the development and maintenance of tension), α_Fx, the force-determined shortening heat, and W, the external work. It is demonstrated that this equation accurately accounts for the time-course of heat evolution and the total initial energy production in both twitches and tetani at 0°C. The force-determined shortening heat is liberated, during shortening, in direct proportion to (a) the distance shortened, and (b) the force against which shortening occurs. The normalized value of the force-determined shortening heat coefficient, α_F/P_o, is the same in both the twitch and the tetanus. Finally, this formulation of the muscle's energy production also accounts for the total energy production in afterload isotonic twitches at 20°C, where a Fenn effect is not demonstrable.     

The qualitative analysis of a difference equation of population growth

The difference equation f _b :[0,1]–[0,1] defined by f _b (x)=b x(1–x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (f _b )ⁱ is given by

Some Theorems Concerning Characterization of the WEIBULL Distribution

This paper presents a number of characterizations of the WEIBULL distribution. Some of these results are generalizations of the corresponding results for the exponential distribution. Some characterizing properties lead to a functional equation f(x) · f(y) = f((x^c+y^c)^i/c) which is analogous to the CAUCHY functional equation. While the first two characterizations assume somewhat less accessible information concerning the probability distribution, the third and fourth require more readily available information regarding the expected values.     

Tunable white light emission from single‐phased Li2SrSiO4:Dy3+ phosphors by co‐doping with Eu3+

A series of single‐phase full‐color emitting Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ phosphors were synthesized by solid‐state reaction and characterized by X‐ray diffraction and photoluminescence analyses. The samples showed emission peaks at 488 nm (blue), 572 nm (yellow), 592 nm (orange) and 617 nm (red) under 393 nm excitation. The photoluminescence excitation spectra, comprising the Eu–O charge transfer band and 4f–4f transition bands of Dy³⁺ and Eu³⁺, range from 200 to 500 nm. The Commission Internationale de I'Eclairage chromaticity coordinates for Li₂Sr_0.98−xSiO₄:0.02Dy³⁺,xEu³⁺ phosphors were simulated. By manipulating Eu³⁺ and Dy³⁺ concentrations, the color points of Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ were tuned from the greenish‐white region to white light and eventually to reddish‐white region, demonstrating that a tunable white light can be obtained by Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ phosphors. Li₂Sr_0.98−xSiO₄:0.02Dy³⁺, xEu³⁺ can serve as a white‐light‐emitting phosphor for phosphor‐converted light‐emitting diode. Copyright © 2014 John Wiley & Sons, Ltd.     

Mechanical properties of the skin of Xenopus laevis (Anura,Amphibia)

The skin of the aquatic pipid frog, Xenopus laevis, was examined for specific biomechanical features: (1) thickness, (2) maximal strain at break (ε_f), (3) tensile strength (σ_m), (4) modulus of elasticity (E, stiffness), and (5) the area under the stress-strain curve (W) (breaking energy, toughness). Skin freshly removed from dorsal, ventral, and lateral areas of the body was subjected to uniaxial tension. In both sexes, the dorsal skin is thicker than the ventral. The skin of male frogs was consistently thinner in all body regions than that of females. Most biomechanical parameters showed a considerable range of values in both males (ε_f = 59–63%, σ_m = 15–16.5 MPa, E = 33.5–38.4 MPa, W = 3.8–4.5 MJ/m³) and females (ε_f = 102–126%, σ_m = 11.5 MPa, E = 10.4–12 MPa, W = 5.2–6.7 MJ/m³). The disparate ε_f values in males (low) and females (high) might reflect sexual dimorphism. Static stress-strain curves were typicxally J-shaped; with the exception of “toe,” the curves rose approximately linearly with increasing strain. The skin of X. laevis, although heterogeneous in structure, possesses features similar to those found in tissues with aligned collagen fibers such as tendons or fish skin. However, in anurans, the skin seems to play a more passive mechanical role during locomotion than in fish. © 1995 Wiley-Liss, Inc.     

Improved Bulk Materials with Thermoelectric Figure‐of‐Merit Greater than 1: Tl10–xSnxTe6 and Tl10–xPbxTe6

Noting the steadily worsening problem of depleted fossil fuel sources, alternate energy sources have become increasingly important; these include thermoelectrics, which may use waste heat to generate electricity. To be economically viable, the thermoelectric figure‐of‐merit, zT, which is related to the energy conversion efficiency, needs to be in excess of unity (zT > 1). Tl₄SnTe₃ and Tl₄PbTe₃ were reported to attain a thermoelectric figure‐of‐merit zT _max = 0.74 and 0.71, respectively, at 673 K. Here, the thermoelectric properties of both materials are presented as a function of x in Tl_10–x Sn _x Te₆ and Tl_10–x Pb _x Te₆, with x varying between 1.9 and 2.05, culminating in zT values in excess of 1.2. These materials are charge balanced when x = 2, according to (Tl⁺)₈(Sn²⁺)₂(Te^2?)₆ and (Tl⁺)₈(Pb²⁺)₂(Te^2?)₆ (or: (Tl⁺)₄Pb²⁺(Te^2?)₃). Increasing x causes an increase in valence electrons, and thus a decrease in the dominating p‐type charge carriers. Larger x values occur with a smaller electrical conductivity and a larger Seebeck coefficient. In each case, the lattice thermal conductivity remains under 0.5 W m^?1 K^?1, resulting in several samples attaining the desired zT _max > 1. The highest values thus far are exhibited by Tl_8.05Sn_1.95Te₆ with zT = 1.26 and Tl_8.10Pb_1.90Te₆ with zT = 1.46 around 685 K.     

Prediction of peak occurrence of Dendrolimus punctatus larvae based on Bayes discriminant method

To improve the accuracy of forecasting the peak occurrence of Dendrolimus punctatus Walker, we here used the Bayes discriminant analysis to predict this peak occurrence for the first and second generation of Dendrolimus punctatus larvae based on these data from 1983 to 2016 in Qianshan County, Anhui Province. Our present results showed that this discriminant equation for the first generation was as follows: f⁽¹⁾ = ?3.2588‐6.2700x₁ + 1.2870x₂ + 0.7920x₃ + 0.4152x₄; f⁽²⁾ = ?14.5215‐8.5710x₁ + 2.9790x₂ + 2.0280x₃ + 0.5031x₄; f⁽³⁾ = ?3.5264; f⁽⁴⁾ = ?66.8312‐12.5216x₁ + 5.1740x₂ + 4.7162x₃ + 0.6033x₄. And that the prediction accuracy for the first generation was 97.22%. Whilst this discriminant equation for the second generation was as follows: f⁽¹⁾ = ?3.536‐1.192x₅ + 1.338x₆ + 0.638x_7?0.025x₈; f⁽²⁾ = ?7.317‐1.337x₅ + 4.240x₆ + 1.010x_7?0.295x₈; f⁽³⁾ = ?16.488‐3.192x₅ + 4.955x₆ + 1.900x₇–0.411x₈; f⁽⁴⁾ = ?34.502‐4.184x₅ + 7.484x₆ + 2.583x₇–0.443x₈. The prediction accuracy for the second generation was 85.71%. Overall, our findings revealed that the Bayes discriminant analysis could screen out key factors to significantly improve the prediction accuracy of peak occurrence of Dendrolimus punctatus larvae.     

Wave speeds of density dependent Nagumo diffusion equations – inspired by oscillating gap-junction conductance in the islets of Langerhans

The equation u_t=(D(u)u_x)_x+f(u) arises in several biological examples and is known to have wave solutions for appropriate D and f. We give here a new formula for finding an approximation to the wave speed, relevant for comparing experiments with model simulations. This is done in details for the simple example D(u)=u+k and an N-shaped f, derived from a model of coupled pancreatic -cells, where the coupling conductance follows the electrical activity as it is found in experiments. On the way, we claim that the wave speed does not depend on the parameter g_K,ATP, mimicking the glucose concentration in the islet, in sharp contrast to the claim set forth in the article by Aslanidi et al. [4].     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

Partitioning of late gestation energy expenditure in ewes using indirect calorimetry and a linear regression approach

Abstract

Late gestation energy expenditure (EE_gest) originates from energy expenditure (EE) of development of conceptus (EE_conceptus) and EE of homeorhetic adaptation of metabolism (EE_homeorhetic). Even though EE_gest is relatively easy to quantify, its partitioning is problematic. In the present study metabolizable energy (ME) intake ranges for twin-bearing ewes were 220 – 440, 350 – 700, 350 – 900 kJ per metabolic body weight (W^0.75) at week seven, five, two pre-partum respectively. Indirect calorimetry and a linear regression approach were used to quantify EE_gest and then partition to EE_conceptus and EE_homeorhetic. Energy expenditure of basal metabolism of the non-gravid tissues (EE_bmng), derived from the intercept of the linear regression equation of retained energy [kJ/W^0.75] and ME intake [kJ/W^0.75], was 298 [kJ/W^0.75]. Values of the intercepts of the regression equations at week seven, five, and two pre-partum were 311, 398, and 451 [kJ/W^0.75], respectively. The difference between the intercepts for different weeks was used to calculate EE_homeorhetic. The remaining part of EE_gest was considered to be EE_conceptus. In conclusion, the good agreement between our values of EE_conceptus and those in the literature indicates the method's validity.     

Optical analysis of Sr3Gd(PO4)3:Pr3+ phosphors for lighting applications

A series of praseodymium (Pr³⁺) ion activated Sr₃Gd_(1−x)(PO₄)₃:xPr³⁺ (0 ≤ x ≤ 2.0 mol%) phosphors were prepared and their structural, compositional and luminescence properties were investigated. The X-ray diffraction profiles indicate that the studied phosphors crystallized into body centred cubic structure and the Pr³⁺ ions have no influence on Sr₃Gd(PO₄)₃ phase. The high-resolution scanning electron microscopy images show the agglomeration of particles that are inter-connected and form irregular shape Sr₃Gd(PO₄)₃ structures. The excitation transitions corresponding to Pr³⁺:³H₄ → ³P_2,1,0 transitions at 445, 471 and 483 nm, respectively, matched well with the emission of blue-light-emitting diode (LED) chip. The emission spectra show strong reddish-orange luminescence through ¹D₂ → ³H₄ transition when excited at 445 nm blue wavelength. The synthesized phosphors have the potential to be used as reddish-orange lighting devices.     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density