Second Derivative Of Function Research Articles

A solution to the singularity problem in the meshless method for neutron diffusion equation

In recent years, the moving least square (MLS) approximation has been widely used for numerical analysis of scattered data. Many numerical methods for solving partial differential equations are developed based on the MLS approximation.The MLS method is ideal for problems where the geometry of the domain is complex. An example of this is the neutron diffusion calculation. The collocation method is known that it has fast convergence speed, however, it is unstable and non-robust in many cases. In particular, it is the reason resulting in the fluctuation of the solution at the position that is on overlapping boundary region. This drawback can be dealt with the meshless local Petrov-Galerkin weak form for nodes on the interface boundary. In this paper, a combination of the weak form of the meshless local Petrov-Galerkin (MLPG) and the collocation method are applied to solve the neutron diffusion equation. Trial functions employed in the weak form of MLPG are constructed via the MLS method. In most MLPG methods numerical integration is required. The exception to this is the case of the collocation method in which the test functions are Dirac delta functions. Therefore, if the shape function is not constructed precisely enough, within an acceptable error range, the second order derivative of the shape function will lack accuracy. One of the reasons for the inaccuracy of the shape function is singularity problems occurring in the process of constructing the shape function. In this study, a solution is introduced to eliminate the singularity problem, allowing us to obtain the derivative of the shape function with sufficient precision. Finally, neutron diffusion problems are implemented in a combination of the weak-form of the meshless local Petrov-Galerkin (MLPG) and the collocation method is used to evaluate the efficiency and accuracy.

Stress integration-based on finite difference method and its application for anisotropic plasticity and distortional hardening under associated and non-associated flow rules

Stress integration algorithm based on finite difference method (FDM) was proposed to effectively deal with both first and second derivatives of yield and potential functions which are the lengthiest component in stress integration procedure. With the proposed numerical algorithm, both first and second derivatives of yield function are approximated by central difference method, so that finite element modeling using advanced constitutive model could be easily performed no matter how complicated its derivatives are. For the verification purpose, the algorithm was applied for advanced constitutive models: Plastic anisotropy model under associated (AFR) and non-associated flow rule (non-AFR), the homogeneous anisotropic hardening (HAH) model under associated (AFR) and non-associated flow rule (non-AFR). The proposed algorithm was verified with single element loading–unloading and cup-drawing simulations. The Euler backward method based on both the proposed numerical algorithm and analytical derivatives were employed for verification purpose. The accuracy and time efficiency of the proposed numerical algorithm were evaluated by comparing the simulation results from analytical derivatives. In addition, the applicability of the proposed numerical algorithm for the HAH models was estimated with single element loading–unloading, loading–reloading, and deep-drawing/springback simulations. Non-associated flow plasticity for the HAH model is newly proposed to improve numerical efficiency with finite difference method by keeping the same level of accuracy as associated flow rule plasticity. All the simulation results proved that the proposed numerical algorithm can be widely used for the implementation of advanced constitutive models.

Chemical hardness: Temperature dependent definitions and reactivity principles.

In this brief report, we show that the three different chemical hardness definitions developed in the framework of the temperature-dependent density functional theory-namely, the electronic, the thermodynamic, and the Helmholtz hardnesses-imply both the hard and soft acids and bases (HSAB) principle and the maximum hardness (MH) principle. These hardnesses are identified as the second derivative of a thermodynamic state function and avoid the somewhat arbitrary approach, based on the parabolic interpolation of the energy versus electron number, that is normally used to justify these principles. This not only leads to a more mathematically sound justification of the HSAB and MH principles in the low-temperature limit but also establishes that the HSAB and the MH principles hold at any temperature of chemical relevance.

Identification of iron in Earth analogues of Martian phyllosilicates using visible reflectance spectroscopy: Spectral derivatives and color parameters

Abstract A range of phyllosilicate compositions have been detected spectroscopically on Mars, but the largest fraction by far corresponds to clay minerals rich in Fe and Mg. Given that most of our understanding of Martian clays comes from remote sensing data, it is critically important to explore the details of how compositional variation affects spectral features of phyllosilicates. The greatest efforts have focused so far on near-infrared (NIR) spectroscopy. Recently, ambiguities have been detected in the NIR spectra of 2:1 phyllosilicates with intermediate Fe Mg content that preclude mineral and chemical discrimination. Such ambiguities highlight the relevance of exploring the visible spectral range as a complementary tool to characterize Martian phyllosilicates precisely. This article reports the investigation of laboratory reflectance spectra (330–800 nm) from 34 Earth analogues of Martian phyllosilicates with a wide range of Mg Fe composition, including nontronite, celadonite and saponite end-members, as well as interstratified glauconite-nontronite, talc-nontronite, and talc-saponite. The spectra indicated the presence of Fe(III) by absorption modulations and a decrease in total reflectance, especially in samples with tetrahedral Fe(III). Absorption bands at 370 and 420 nm were diagnostic of octahedrically and tetrahedrally coordinated Fe(III), respectively. Band amplitudes in the second derivative of the Kubelka-Munk function correlated positively with Fe(III) content (R2 > 0.8). Standard color analyses of the visible reflectance spectra under the CIE illuminant D65 indicated that the CIELAB color parameter a*10 was positively correlated with tetrahedral Fe(III), b*10 was positively correlated with octahedral Fe(III), and L*10 was negatively correlated with Fe(III) in both structural sites. Because Fe(II) was in relatively low amount, it did not provide clear spectral evidence. Multiple regression models using the amplitude of the diagnostic absorption bands predicted well absolute Fe content in the phyllosilicates (R2 = 0.89) and the ratio Fe/(Fe + Mg + Al) (R2 = 0.84). CIELAB color parameters improved the prediction of total Fe (R2 = 0.92) and the ratio Fe/(Fe + Mg + Al) (R2 = 0.93). Application of these analyses to Martian data has challenges set by Fe oxide dust coating and spatial and spectral resolution. However, these results mark an avenue to develop testable tools using visible-wavelength spectral data from both satellite and lander probes to help establishing Fe content and mineral identification of Martian phyllosilicates.

Dependence of bottlenose dolphin (Tursiops truncatus) auditory brainstem responses on noise burst rise time, amplitude, and envelope shape

A series of experiments examined the dependence of dolphin auditory brainstem response (ABR) peak amplitudes and latencies by stimulus level, rise times, and envelope shape. Stimuli were spectrally “pink” noise bursts with frequency content from 10 to 160 kHz, rise times that varied from 32 μs to 4 ms, and plateau sound pressure levels from 102 to 138 dB re 1 μPa. Cosine and cosine-cubed rise (and fall) envelopes were tested, and results were compared to those obtained for dolphins using noise bursts with linear rise envelopes [Finneran et al., J. Acoust. Soc. Am. 143, 2914–2921 (2018)]. Results for the cosine and cosine-cubed envelopes showed that ABR peak amplitudes were a function of envelope sound pressure at the end of a fixed integration window of approximately 260 μs. This is congruent with the previous findings for linear envelopes. The ABR peak latencies for the cosine and cosine-cubed envelopes were dependent on the second derivative of the envelope pressure function, as opposed to the first derivative of the pressure function for linear envelopes. These data are consistent with single-unit and nearfield response data for terrestrial mammals. [Work supported by Navy Living Marine Resources and SSC Pacific Naval Innovative Science and Engineering Programs.]

Differential representation of the delta function in two-dimensional quantum mechanics

The exactly solvable model of a two-dimensional system consisting of a particle in a Dirac delta function potential is studied in position space in lieu of momentum space. This study is facilitated by representing the delta function as the second derivative of a radial function, which depends on a length scale. Such a representation of the delta function provides an instructive approach to understanding the role of an arbitrary length scale in the concepts of regularization and renormalization.

Criterion for quantum Zeno and anti-Zeno effects

In this work, we study the decay behavior of a two-level system under the competing influence of a dissipative environment and repetitive measurements. The sign of the second derivative of the environmental spectral density function with respect to the system transition frequency is found to be a sufficient condition to distinguish between the quantum Zeno (negative) and the anti-Zeno (positive) effects raised by the measurements. We check our criterion for practical measurement intervals, which are larger than the conceptual Zeno time, in various environments. In particular, with the Lorentzian spectrum, the quantum Zeno and anti-Zeno phenomena are found to emerge respectively in the near-resonant and off-resonant cases. For the interacting spectra of hydrogenlike atoms, the quantum Zeno effect usually occurs and the anti-Zeno effect can rarely occur unless the transition frequency is close to the cut-off frequency. With a power-law spectrum, we find that sub-Ohmic and super-Ohmic environments lead to the quantum Zeno and anti-Zeno effects, respectively.

Nonlocal kinetic energy functionals by functional integration.

Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δTs[ρ]δρ(r), yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.

Shape preserving constrained and monotonic rational quintic fractal interpolation functions

Shape preserving interpolants play important role in applied science and engineering. In this paper, we develop a new class of $${\mathscr {C}}^2$$ -rational quintic fractal interpolation function (RQFIF) by using rational quintic functions of the form $$\frac{p_i(t)}{q_i(t)},$$ where $$p_i(t)$$ is a quintic polynomial and $$q_i(t)$$ is a cubic polynomial with two shape parameters. The convergent result of the RQFIF to a data generating function in $${\mathscr {C}}^3$$ is presented. We derive simple restrictions on the scaling factors and shape parameters such that the developed rational quintic FIF lies above a straight line when the interpolation data with positive functional values satisfy the same constraint. Developing the relation between the attractors of equivalent dynamical systems, the constrained RQFIF can be extended to any general data. The positivity preserving RQFIF is a particular case of our result. In addition to this we also deduce the range on the IFS parameters to preserve the monotonicity aspect of given restricted type of monotonic data. The second derivative of the proposed RQFIF is irregular in a finite or dense subset of the interpolation interval, and matches with the second derivative of the classical rational quintic interpolation function whenever all scaling factors are zero. Thus, our scheme outperforms the corresponding classical counterpart, and the flexibility offered through the scaling factors is demonstrated through suitable examples.

Analysis of the influence of train load characteristics on the water damage of slab tracks

High-speed train load is one of the main factors that causes the failure of a slab track and is also the direct cause for producing water pressure in the cracks. Hence, choosing the right loading method is the key to analyze the water damage of slab tracks. In order to identify the distribution characteristics of the vertical force acting on the slab track, the analytic expression of fastener load was derived, and the field test was conducted to verify the theoretical model. According to the distribution characteristics of fastener load and the area of crack filled with water, the loading method was presented to analyze the water damage of slab tracks, and the influence of loading characteristics on the hydrodynamic pressure and crack propagation was analyzed. The results show that the distribution of fastener load in the main affected zone approximately accords with the Gaussian distribution under the single wheel load. When under the action of double wheels, the superimposed effect makes the second derivative of the loading function to increase by 99.93%. The superimposed effect of three or more wheels is less than 1% and can be ignored. Considering that the hydrodynamic pressure is highly sensitive to the second derivative of loading function, the load applied on the track slab should be in the form of a bogie, and different loads should be applied step by step based on the time series. The distribution of hydrodynamic pressure along the crack is approximately equal to the cubic polynomial, and the pressure peak appears at the crack tip. Also, the pressure is proportional to the square of the running speed of the train. In the region with abundant rainwater and a poor drainage system, reducing the train speed and taking timely measures such as grouting can effectively reduce the water damage of slab tracks.

Topology optimization of density type for a linear elastic body by using the second derivative of a KS function with respect to von Mises stress

This study demonstrates the use of Newton method to solve topology optimization problems of density type for linear elastic bodies to minimize the maximum von Mises stress. We use the Kreisselmeier–Steinhauser (KS) function with respect to von Mises stress as a cost function to avoid the non-differentiability of the maximum von Mises stress. For the design variable, we use a function defined in the domain of a linear elastic body with no restriction on the range and assume that a density is given by a sigmoid function of the function of design variable. The main aim of this study involves evaluating the second derivative of the KS function with respect to variation of the design variable and to propose an iterative scheme based on an H1 Newton method as opposed to the H1 gradient method that was presented in previous studies. The effectiveness of the scheme is demonstrated by numerical results for several linear elastic problems. The numerical results show that the speed of the proposed H1 Newton method exceeds that of the H1 gradient method.

The Second Partial Derivative of Option Price with Respect to the Strike: A Historical Reminiscence

An option’s market price reflects the risk-neutral probability that it will end up in the money. Research has been increasing in recent years that shows how, given a set of market prices for options covering a range of strikes, an estimate of the entire risk-neutral probability distribution can be obtained. The technique is based on the fact that the second partial derivative of the option pricing function with respect to the strike price is the risk-neutral density (discounted from option expiration). This idea is generally attributed to Breeden and Litzenberger’s 1978 paper. In this article, Zimmermann shows that the connection between the second partial derivative of the option price with respect to the exercise price and risk-neutral probabilities has a much longer history, including a little-known 1974 note by Fischer Black, and going all the way back to Bachelier in 1900.

Mixed discrete least squares meshless method for solving the linear and non-linear propagation problems

A Mixed formulation of Discrete Least Squares Meshless (MDLSM) as a truly meshfree method is presented in this paper for solving both linear and non-linear propagation problems. In DLSM method, the irreducible formulation was deployed which needs to calculate the costly second derivatives of the MLS shape functions. In the proposed MDLSM method, the complex and costly second derivatives of shape functions are not required. Furthermore, using the mixed formulation, both unknown parameters and their gradients are simultaneously obtained circumventing the need for post-processing procedure performed in irreducible formulation to calculate the gradients. Therefore, the accuracy of gradients of unknown parameters is increased. In MDLSM method, the set of simultaneous algebraic equations are built by minimizing a least squares functional with respect to the nodal parameters. The least squares functional defined as the sum of squared residuals of the differential equation and its boundary condition. The proposed method automatically leads to symmetric and positive-definite system of equations and, therefore, is not subject to the Ladyzenskaja-Babuska-Brezzi (LBB) condition. The proposed MDLSM method is validated and verified by a set of benchmark problems. The results indicate the ability of proposed method to efficiently and effectively solve the linear and non-linear propagation problems.

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f(ϕ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass MCS. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ⟨ γ γ ζ ⟩ for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f(ϕ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

Effects of S-doping on the electronic transition, band gap, and optical absorption of GaSe1−xSx single crystals

The intrinsic evolutions of electronic transition and the band gap of GaSe1−xSx solid solution single crystals (x = 0, 0.133, and 0.439) grown for nonlinear optical applications have been systemically investigated by using spectroscopic ellipsometry and first-principle calculations. Five interband electronic transitions E1, E2, E3, E4, and E5 have been obtained by fitting the second derivatives of the complex dielectric functions and the physical origins were explained with the aid of theoretical calculations. It is found that the interband electronic transition energy E2, E3, and E4 show a blueshift trend from 3.457 eV, 3.736 eV, and 4.810 eV at x = 0 to 3.786 eV, 4.628 eV, and 5.086 eV at x = 0.439, respectively. This is because the larger Se atoms are replaced by smaller S atoms in GaSe1−xSx. The experimental band gap of GaSe1−xSx is increased from 1.908 eV at x = 0 to 2.081 eV at x = 0.439. Moreover, in order to verify the influences of S-doping on the band gap of GaSe1-xSx, we performed the first-principle calculations based on the density-functional theory. The theoretical results also confirm that the band gap energy increases from 2.085 eV at x = 0 to 2.15 eV at x = 0.439, which is in good agreement with the experiment results.

Numerical implementation of a modified Mohr\u2013Coulomb model and its application in slope stability analysis

The hyperbolic function proposed by Abbo–Sloan was employed not only to approach the Mohr–Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr–Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-dimensional user subroutines which can consider the associated or non-associated flow rule were developed on the platform of the finite element program—ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr–Coulomb model and the analytical approach. Then the main influential factors including the associated or non-associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the stability analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.

Computation of pseudospectral abscissa for large-scale nonlinear eigenvalue problems

Author(s): Meerbergen, K; Michiels, W; Van Beeumen, R; Mengi, E | Abstract: We present an algorithm to compute the pseudospectral abscissa for a nonlinear eigenvalue problem. The algorithm relies on global under-estimator and over-estimator functions for the eigenvalue and singular value functions involved. These global models follow from eigenvalue perturbation theory. The algorithm has three particular features. First, it converges to the globally rightmost point of the pseudospectrum, and it is immune to nonsmoothness. The global convergence assertion is under the assumption that a global lower bound is available for the second derivative of a singular value function depending on one parameter. It may not be easy to deduce such a lower bound analytically, but assigning large negative values works robustly in practice. Second, it is applicable to large-scale problems since the dominant cost per iteration stems from computing the smallest singular value and associated singular vectors, for which efficient iterative solvers can be used. Furthermore, a significant increase in computational efficiency can be obtained by subspace acceleration, that is, by restricting the domains of the linear maps associated with the matrices involved to small but suitable subspaces, and solving the resulting reduced problems. Occasional restarts of these subspaces further enhance the efficiency for large-scale problems. Finally, in contrast to existing iterative approaches based on constructing low-rank perturbations and rightmost eigenvalue computations, the algorithm relies on computing only singular values of complex matrices. Hence, the algorithm does not require solutions of nonlinear eigenvalue problems, thereby further increasing efficiency and reliability. This work is accompanied by a robust implementation of the algorithm that is publicly available.

First-Principles Prediction of Electronic, Magnetic, and Optical Properties of Co2MnAs Full-Heusler Half-Metallic Compound

Electronic, magnetic, and optical properties of Co2MnAs full-Heusler compound have been calculated using a first-principles approach with the full-potential linearized augmented plane-wave (FP-LAPW) method and generalized gradient approximation plus U (GGA + U). The results are compared with various properties of Co2MnZ (Z = Si, Ge, Al, Ga, Sn) full-Heusler compounds. The results of our calculations show that Co2MnAs is a half-metallic ferromagnetic compound with 100% spin polarization at the Fermi level. The total magnetic moment and half-metallic gap of Co2MnAs compound are found to be 6.00μB and 0.43 eV, respectively. It is also predicted that the spin-wave stiffness constant and Curie temperature of Co2MnAs compound are about 3.99 meV nm2 and 1109 K, respectively. The optical results show that the dominant behavior, at energy below 2 eV, is due to interactions of free electrons in the system. Interband optical transitions have been calculated based on the imaginary part of the dielectric function and analysis of critical points in the second energy derivative of the dielectric function. The results show that there is more than one plasmon energy for Co2MnAs compound, with the highest occurring at 25 eV. Also, the refractive index variations and optical reflectivity for radiation at normal incidence are calculated for Co2MnAs. Because of its high magnetic moment, high Curie temperature, and 100% spin polarization at the Fermi level as well as its optical properties, Co2MnAs is a good candidate for use in spintronic components and magnetooptical devices.

19 A NOVEL APPROACH TO COMPARING REPRODUCTIVE STAGE SERUM PROFILES IN MARES USING NEAR-INFRARED SPECTROSCOPY AND AQUAPHOTOMICS

The capability of near-infrared spectroscopy (NIR) to detect biomolecules in aqueous solutions, a sub-field of NIR called aquaphotomics, has yet to be fully explored. Aquaphotomics references water absorbance patterns and wavelength shifts in the 1st overtone of the water spectrum as they change patterns with solute composition and concentrations. Recently, NIR was used as a rapid method for detecting oestrus in Holstein raw milk and for monitoring reproductive stages in urine of the Bornean Orangutan (Pongo pygmaeus) and the giant panda (Ailuropoda melanoleuca). Near-infrared spectroscopy detects bond vibrations from organic molecules and water to create unique absorbance patterns, which are used to profile complex mixtures of biomolecules. The objectives of this study are to (1) characterise serum NIR spectral profiles for oestrus, metestrus, and diestrus in mares, and (2) determine if NIR can accurately decipher these reproductive phases from serum due to the biochemical effects of reproductive hormones. Mare oestrus cycles were assessed every other day by ultrasound and serum hormone analysis. Serum was collected via jugular venipuncture on day 0, 2, 4, 8, and 16 of each cycle for 3 consecutive cycles from each mare. Radioimmunoassay analysis of reproductive hormones E2 and P4 was used to validate and characterise the NIR spectra. Spectra were collected from triplicate samples of 200 μL of serum in a 1-mm-path-length quartz cuvette with an ADS FieldSpec®3 spectrophotometer, at room temperature (22°C). Chemometric analysis (Unscrambler® X v.10.4; CAMO Software) included pretreatment with a Savitsky-Golay second-derivative function for visual inspection of spectral features and principal component analysis (PCA), after mean centering, for distinction of reproductive status. Spectral peaks at 1347, 1367, and 1465 nm were unique to serum collected from mares in oestrus exhibiting high E2 (11.87 to 16.88 pg mL−1). Early metestrus is characterised by prominent spectral peaks at 1383 and 1437 nm, corresponding to E2 levels (0.02 to 5.29 pg mL−1) and P4 levels (0.02 to 3.61 ng mL−1). Diestrus peaks were found at 1342, 1426, and 1473 nm, when P4 levels ranged from 5.14 to 9.60 ng mL−1. In our PCA models, 98% of the total variance in serum spectra between any pair of reproductive phases was described in only 3 spectral PCs, (PC1 = 83–86%, PC2 = 9–10%, PC3 = 2–5% of total variance). The PCA scores separated into distinct groups, indicating clear spectral profiles describing each reproductive phase uniquely. In conclusion, PCA analysis and spectral variances indicate that NIR, specifically aquaphotomics, has the theoretical capability to discriminate complex mixtures of biomolecules present in mare serum during oestrus, metestrus, and diestrus reproductive states. Study was supported by USDA-ARS Biophotonics Initiative grant #58-6402-3-018.

A New Descriptive Statistic for Functional Data: Functional Coefficient Of Variation

Bu calismada fonksiyonel veriler icin yeni bir tanimlayici istatistik olan degiskenlik katsayisi fonksiyonunu onermekteyiz. Ozellikle her bir egri grubunun ortalama fonksiyonlari farkli oldugu durumda, coklu egri gruplarinin degiskenliklerini karsilastirmada onerilen degiskenlik katsayisi fonksiyonunun kullanilmasini tavsiye ediyoruz. Degiskenlik katsayisi fonksiyonunu elde ederken kubik B-Splaynlar kullanildigindan dolayi, bu fonksiyonlarin birinci ve ikinci turev fonksiyonlarinin da yorumlanabiliyor olmasi, orijinal egriler hakkinda daha guclu cikarimlar yapabilmemizi saglamaktadir. Onerilen istatistigin kullanimi ve etkileri literaturdeki iyi bilinen bir veri seti uzerinde raporlanmistir. Sonuclar gostermektedir ki onerilen istatistik verinin degiskenligini duzgun bir sekilde yansitmaktadir ve bu durum ortalama fonksiyonlari farklilastikca standart sapma fonksiyonundan daha ustun bir hale gelmektedir.