The field equation following the non-linear Lagrangian -2L + R + aR2 has been considered as an alternative to Einstein's theory. Based on the background field method, the linearized fourth ORDER field equation has been obtained in both the 4-dimensional de Sitter space-time and the flat 5-dimensional ambient space notations. The field equation has been projected into the Minkowskian 4-dimensional space by taking the zero curvature limit. It has been shown that the field equation transforms according to one of the unitary irreducible representations of de Sitter group denoted by P 2,2±, in discreet series.

Background: Pterygium causes visual disturbance due to ocular surface irregularity. The convenient method to investigate this irregularity is measurement of ocular aberration. The aim of this study to investigate the impact of pterygium excision with conjunctival autograft together with corneal polishing on ocular HIGHER-ORDER aberrations (HOAs). Methods: This study was performed on 34 patients with primary nasal pterygium who had an indication for surgical excision in November 2013. All patients underwent a detailed ophthalmologic examination preoperatively and at the third postoperative months. Pterygium excision was performed by the same surgeon. Corneal topography and ocular HIGHER-ORDER aberration were measured by ITRACE. Results: Numerous parameters including mean value cylinder and spherical refractive error, visual acuity, root mean square values of total HOAs were found to be significantly improved at 3 month after pterygium surgery. There was significant difference between preoperative and postoperative mean refractive cylinder (-6. 77 ± 1. 08 diopter (D) vs. 2. 25 ± 0. 34 diopter (D), respectively, P < 0. 0001). Log Mar best corrected visual acuity (0. 11± 0. 03) was significantly HIGHER than preoperative values (0. 04± 0. 02)(p<0. 001). Preoperative mean refractive sphere was 4. 92± 0. 79 diopter (D) which was significantly HIGHER than postoperative refractive sphere 0. 66± 0. 41 diopter (D) (P< 0. 0001). All parameters (Total, Lo total, Defocus, Astigmatism, Coma, Trefoil: P<0. 001 and Ho total: P=0. 001 and secondary: P=0. 04) except for total spherical aberration (P = 0. 38) were found to be lower when compared with the preoperative values. . None of the patient harbor against the rule astigmatism preoperatively and a significant scope of with the rule cases changed to oblique astigmatism at 3 month which statistically significant (P<0. 001). Conclusion: Pterygium excision can significantly improve visual acuity and most of the pterygium-induced HOAs.

Purpose: To evaluate the correlation between refractive error and HIGHER-ORDER aberrations (HOAs) in patients with myopic astigmatism.Methods: HOAs were measured using the Zywave II aberrometer over a 6 mm pupil. Correlations between HOAs and myopia, astigmatism, and age were analyzed.Results: One hundred and twenty-six eyes of 63 subjects with mean age of 26.4±5.9 years were studied. Mean spherical equivalent refractive error and refractive astigmatism were -4.94±1.63 D and 0.96±1.06 D, respectively. The most common HIGHER-ORDER aberration was primary horizontal trefoil with mean value of 0.069±0.152 mm followed by spherical aberration (-0.064±0.130 mm) and primary vertical coma (-0.038±0.148 mm). As the ORDER of aberration increased from third to fifth, its contribution to total HOA decreased: 53.9% for third ORDER, 31.9% for fourth ORDER, and 14.2% for fifth ORDER aberrations. Significant correlations were observed between spherical equivalent refractive error and primary horizontal coma (R=0.231, P=0.022), and root mean square (RMS) of spherical aberration (R=0.213, P=0.031); between astigmatism and RMS of total HOA (R=0.251, P=0.032), RMS of fourth ORDER aberration (R=0.35, P<0.001), and primary horizontal coma (R=0.314, P=0.004). Spherical aberration (R=0.214, P=0.034) and secondary vertical coma (R=0.203, P=0.031) significantly increased with age. Conclusion: Primary horizontal trefoil, spherical aberration and primary vertical coma are the predominant HIGHER-ORDER aberrations in eyes with myopic astigmatism.

We can explain “knowing” in Avicenna's thought through HIGHER-ORDER consciousness. He admits unconscious perception both in innate human knowledge namely self-awareness and self-evident concepts and propositions and in sense perceptions, imaginary perceptions, and intellectual perceptions. The difference between conscious and unconscious perceptions is due to the presence of self as the spectator of perception in the earlier and the absence of that in the later. So acquiring knowledge is possible only through presence, attention, and intention of self, hence one knows that she knows. So “knowing” requires HIGHER-ORDER consciousness.

risk & return are two main factors that affect financial decisions. The trade off between risk & return create different investment strategies. In other words investment decisions are all based on risk & return. In this research we used multiperiod selection method in ORDER to maximize investors utility. In this model we used not only variance but also HIGHER ORDER moment – skewness-for optimization. For emprical test of the model we used return of first 50 companies stored by market capitalization in tehran stock exchange during 1386-1395. We used skewness & transaction cost to introduce a moltipriod model in asset allocation to minimize variance of investors utility. Comparing the result of this model with markowitz model & simpel model considering investor preferences shows that based on performance evaluation criteria, the suggested model perform much better than the two other.

In this paper we consider the action of HIGHER derivative GRAVITY up to the second ORDER terms in the scalars made from the Ricci scalar, Ricci and Riemann tensors. We use the Bach- Lanczos identity of the Weyl tensor in four dimensions and show that the solutions of 4-dimensional Einstein equations with cosmological constant term in vacuum, which are known as Einstein metrics, satisfy the field equations of HIGHER derivative GRAVITY. We also find that the field equations of HIGHER derivative GRAVITY are not satisfied by the solutions of Einstein equations in HIGHER dimensions or in the presence of matter.

Purpose: To investigate the relationship between HIGHER-ORDER aberrations (HOAs) and contrast sensitivity function (CSF) in myopes.Methods: In this cross-sectional study, HOAs and CSF were measured in myopic eyes over a 6-mm pupil. Pupil diameter was measured in photopic condition. The correlation between HOAs and CSF was investigated using multivariate linear regression analysis.Results: Seventy right myopic eyes of 70 subjects with a mean age of 26.6±5.7 years were studied. Mean spherical equivalent (SE) and refractive astigmatism were -4.97±1.6 D and 0.93±0.5 D, respectively. AULCSF was significantly but indirectly correlated with cycloplegic SE (R2=0.57, P=0.02), the root mean square (RMS) of total HOA (R2=0.065, P=0.03), 4th-ORDER aberration (R2=0.089, P=0.015) and spherical aberration (R2=0.037, P=0.004). AULCSF had no significant association with age, photopic pupil diameter, refractive astigmatism, and RMS of coma aberration.Conclusion: Spherical and 4th-ORDER aberrations significantly affect contrast sensitivity function. However, other factors such as neural elements of visual pathway may have a role.

A new HIGHER-ORDER triangular plane element with drilling degrees of freedom is proposed by assumption of second-ORDER strain field. In addition to inclusion of drilling degrees of freedom and utilization of HIGHER-ORDER assumes strains, satisfaction of equilibrium equations improves performance of the suggested element in comparison with many of the other available elements. After proposition of the new element, a series of benchmark problems are solved to evaluate performance of the suggested element. Accuracy and efficiency of the suggested element is compared with other strain-based plane elements. Detailed discussions are offered after each benchmark problem. Finally, based on the attained results, a final conclusion about characteristics of robust membrane elements is made.

A novel approach to surface electromyogram (sEMG) signal classification using its HIGHER ORDER statistics (HOS) is presented in this study. As the probability density function of the sEMG during isometric contraction in some cases is very close to the Gaussian distribution, it is frequently assumed to be Gaussian. As this assumption is not valid when the force is small, in this paper, we consider the non-Gaussian characteristics of the sEMG, and compute the second-, the third- and the fourth ORDER statistics of the sEMG as its features. These features are used to classify four upper limb primitive motions, i.e., elbow flexion (EF), elbow extension (EE), forearm supination (FS), and forearm pronation (FP). We used the sequential forward selection (SFS) method to reduce the number of HOS features to a sufficient minimum while retaining their discriminatory information, and apply the Knearest neighbor method for classification. Our approach is robust against statistical variations in noise, and does not require additional computations compared to existing methods for providing high rates of correct classification of the sEMG, which makes it useful in devising real-time sEMG controlled prostheses.