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Showing papers by "Hengyang Normal University published in 2014"


Book ChapterDOI
06 Sep 2014
TL;DR: Experimental results demonstrate the effectiveness of SFV, and the combination of the traditional FV and SFV outperforms state-of-the-art methods on these datasets with a large margin.
Abstract: Representation of video is a vital problem in action recognition. This paper proposes Stacked Fisher Vectors (SFV), a new representation with multi-layer nested Fisher vector encoding, for action recognition. In the first layer, we densely sample large subvolumes from input videos, extract local features, and encode them using Fisher vectors (FVs). The second layer compresses the FVs of subvolumes obtained in previous layer, and then encodes them again with Fisher vectors. Compared with standard FV, SFV allows refining the representation and abstracting semantic information in a hierarchical way. Compared with recent mid-level based action representations, SFV need not to mine discriminative action parts but can preserve mid-level information through Fisher vector encoding in higher layer. We evaluate the proposed methods on three challenging datasets, namely Youtube, J-HMDB, and HMDB51. Experimental results demonstrate the effectiveness of SFV, and the combination of the traditional FV and SFV outperforms state-of-the-art methods on these datasets with a large margin.

404 citations


Journal ArticleDOI
TL;DR: Based on the high sensitivity and good selectivity of the Pd/GO modified electrode, the proposed method was successfully applied to the determination of paracetamol in commercial tablets and human urines, and the satisfactory results confirm the applicability of this sensor in practical analysis.

148 citations


Journal ArticleDOI
TL;DR: A novel electrochemical sensor based on an acetylene black paste electrode modified with molecularly imprinted chitosan-graphene composite film for sensitive and selective detection of bisphenol A (BPA) has been developed and successfully employed to detect BPA in plastic bottled drinking water and canned beverages.

112 citations


Book ChapterDOI
06 Sep 2014
TL;DR: A high-order VLAD (H-VLAD) for visual recognition is proposed, which leverages two kinds of high- order statistics in the VL AD-like framework, namely diagonal covariance and skewness and allows for efficient computation.
Abstract: Recent studies show that aggregating local descriptors into super vector yields effective representation for retrieval and classification tasks. A popular method along this line is vector of locally aggregated descriptors (VLAD), which aggregates the residuals between descriptors and visual words. However, original VLAD ignores high-order statistics of local descriptors and its dictionary may not be optimal for classification tasks. In this paper, we address these problems by utilizing high-order statistics of local descriptors and peforming supervised dictionary learning. The main contributions are twofold. Firstly, we propose a high-order VLAD (H-VLAD) for visual recognition, which leverages two kinds of high-order statistics in the VLAD-like framework, namely diagonal covariance and skewness. These high-order statistics provide complementary information for VLAD and allow for efficient computation. Secondly, to further boost the performance of H-VLAD, we design a supervised dictionary learning algorithm to discriminatively refine the dictionary, which can be also extended for other super vector based encoding methods. We examine the effectiveness of our methods in image-based object categorization and video-based action recognition. Extensive experiments on PASCAL VOC 2007, HMDB51, and UCF101 datasets exhibit that our method achieves the state-of-the-art performance on both tasks.

76 citations


Journal ArticleDOI
TL;DR: A reliable sensor was fabricated by modifying an acetylene black paste electrode with graphene (denoted as GR/ABPE) for sensitive and selective determination of tryptophan (Trp) and showed a strong enhancement effect on the oxidation of Trp, and greatly increased the peak current.

58 citations


Journal ArticleDOI
TL;DR: In this paper, a simple and sensitive voltammetric method for the simultaneous determination of 2-nitrophenol and 4-nitrophenol was described, which is based on the use of an acetylene black paste electrode modified with a graphene-chitosan composite film (denoted as Gr-Chit/ABPE).
Abstract: We describe a simple and sensitive voltammetric method for the simultaneous determination of 2-nitrophenol and 4-nitrophenol. It is based on the use of an acetylene black paste electrode modified with a graphene-chitosan composite film (denoted as Gr-Chit/ABPE). The reduction peak currents of 2-nitrophenol (at −252 mV) and of 4-nitrophenol (at −340 mV) in pH 1.0 solution increase significantly at the Gr-Chit/ABPE in comparison to a bare ABPE. Factors affecting sensitivity were optimized and a linear relationship is found between peak current and the concentrations of 2-nitrophenol (in the 0.4 μM to 80 μM range) and for 4-nitrophenol (in the 0.1 μM to 80 μM range). The detection limits (at an SNR of 3 and after a 30-s accumulation time) are 200 nM for 2-nitrophenol and 80 nM for 4-nitrophenol, respectively. The modified electrode was successfully applied to the direct and parallel determination of 2-nitrophenol and 4-nitrophenol in spiked water samples.

50 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback, and they obtained a unique global solution under suitable assumptions on the kernel g.
Abstract: In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation $$u_{tt}(x, t) - \Delta {u}(x, t) + \int_{0}^{t} g(t - s)\,\Delta {u}(x, s){\rm d}s + \mu_{1} u_{t}(x, t) + \mu_{2} u_{t}(x, t -\tau) = 0$$ together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561–1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065–1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065–1082, 2011).

49 citations


Journal ArticleDOI
TL;DR: In this article, the spin-dependent splitting in intrinsic photonic spin Hall effect has been investigated and shown to be tunable by breaking the rotational symmetry of a cylindrical vector beam.
Abstract: We report the realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect. By breaking the rotational symmetry of a cylindrical vector beam, the intrinsic vortex phases that the two spin components of the vector beam carries, which is similar to the geometric Pancharatnam-Berry phase, are no longer continuous in the azimuthal direction, and leads to observation of spin accumulation at the opposite edge of the beam. Due to the inherent nature of the phase and independency of light-matter interaction, the observed photonic spin Hall effect is intrinsic. Modulating the topological charge of the vector beam, the spin-dependent splitting can be enhanced and the direction of spin accumulation is switchable. Our findings may provide a possible route for generation and manipulation of spin-polarized photons, and enables spin-based photonics applications.

40 citations


Journal ArticleDOI
TL;DR: In this article, the CuI/triethanolamine catalyst system efficiently promotes the direct hydroxylation of aryl iodides and bromides in water to provide the corresponding phenols in good to excellent yields.

36 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of analytic and univalent functions in the unit disk |z| < 1 satisfying the condition that the Koebe function is convex in some direction.
Abstract: Lawrence Zalcman’s conjecture states that if \({f(z)=z+\sum olimits_{n=2}^{\infty}a_{n}z^{n}}\) is analytic and univalent in the unit disk \({|z|<1}\), then \({|a_n^2-a_{2n-1}|\leq (n-1)^2,}\) for each \({n\geq 2}\), with equality only for the Koebe function \({k(z)=z/(1-z)^2}\) and its rotations. This conjecture remains open although it has been verified for a few geometric subclasses of the class of univalent analytic functions. In this paper, we consider this problem for the family of normalized functions f analytic and univalent in the unit disk |z| < 1 satisfying the condition $${\rm Re }\left( 1+\frac{zf''(z)}{f'(z)}\right) > -\frac{1}{2}\,\,\,\,\,{\rm for}\,\,\,\,\,|z|<1.$$ Functions satisfying this condition are known to be convex in some direction (and hence close-to-convex and univalent) in |z| < 1. A few other related basic results and remarks about the Hayman index of functions in this family are also presented.

29 citations


Journal ArticleDOI
TL;DR: The systematical work, including experimental measurements and theoretical confirmation, proves that such unusual room temperature ferromagnetism in hexagonal boron nitride nanosheets is edge-dependent, similar to widely reported graphene-based materials.
Abstract: Understanding the mechanism of ferromagnetism in hexagonal boron nitride nanosheets, which possess only s and p electrons in comparison with normal ferromagnets based on localized d or f electrons, is a current challenge In this work, we report an experimental finding that the ferromagnetic coupling is an intrinsic property of hexagonal boron nitride nanosheets, which has never been reported before Moreover, we further confirm it from ab initio calculations We show that the measured ferromagnetism should be attributed to the localized π states at edges, where the electron-electron interaction plays the role in this ferromagnetic ordering More importantly, we demonstrate such edge-induced ferromagnetism causes a high Curie temperature well above room temperature Our systematical work, including experimental measurements and theoretical confirmation, proves that such unusual room temperature ferromagnetism in hexagonal boron nitride nanosheets is edge-dependent, similar to widely reported graphene-based materials It is believed that this work will open new perspectives for hexagonal boron nitride spintronic devices

Journal ArticleDOI
TL;DR: In this article, a host-guest electrochemical platform for sensing the pollutant 1,3-dinitrobenzene was presented based on the use of a glassy carbon electrode (GCE) covered with a composite made from multiwalled carbon nanotubes and graphene oxide, and functionalized with β-cyclodextrin (β-CD).
Abstract: We are presenting a host-guest electrochemical platform for sensing the pollutant 1,3-dinitrobenzene. The method is based on the use of a glassy carbon electrode (GCE) covered with a composite made from multiwalled carbon nanotubes and graphene oxide, and functionalized with β-cyclodextrin (β-CD). The resultant composite was characterized by scanning electron microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis and electrochemical techniques. The modified GCE was used for the sensitive detection of 1,3-dinitrobenzene (DNB) at working voltages of −355 mV and −483 mV. Due to the specific recognition property of β-CD and the excellent electronic properties of the carbon nanomaterials, the electrode exhibits outstanding supramolecular recognition and enhanced electrochemical response to DNB compared to more conventional electrodes. Under optimum conditions, the peak currents vary linearly with the DNB concentrations in the range from 0.02 to 30.0 μM, and the detection limit is 5.0 nM (at an S/N of 3). The electrode exhibits long-term stability and has been successfully applied to the determination of DNB in spiked soil and water samples.

Journal ArticleDOI
Deping Wang1, Kuang Daizhi1, Zhang Fuxing1, Yang Liu1, Shunhua Ning1 
TL;DR: An efficient protocol for ligand-free Cu-catalyzed N-arylation of heteroarylamines has been developed and is particularly suitable for reactions of the most hindered aryl iodides with 2-aminopyridines.

Journal ArticleDOI
TL;DR: Binding kinetic experiments demonstrated that the 2D imprinting approach can improve site accessibility for the template effectively and when using MIM as a stationary phase for HPLC, baseline separation of cholesterol from other compounds can be achieved.
Abstract: The two-dimensional (2D) molecular imprinting approach has attracted extensive research interest in recent years due to its potential advantages such as simple construction, fast template removal and rapid mass transfer. In this study, a new 2D imprinting approach based on the combination of mesoporous silica materials and molecular imprinting technology is reported. 2D molecularly imprinted materials (MIMs) for cholesterol were prepared by using cholesterol as the template, azide modified β-cyclodextrin (azide-β-CD) as the functional monomer and alkynyl-modified SBA-15 (alkyne-SBA-15) as the skeleton. In this method, azide-β-CD molecules were first assembled around the templates by formation of template–monomer complexes, and thus the mutual positions of azide-β-CD molecules were fixed. Then, azide-β-CD molecules were anchored to the walls of the nano-pores of SBA-15 via click chemistry. After removal of the template molecules, the resulting cavities, i.e., recognition sites were formed in the nano-pores of mesoporous silicas. The synthesized MIM was characterized by FT-IR, X-ray diffraction (XRD), elemental analysis (EA), thermal gravimetric analysis (TGA), scanning electron microscopy (SEM) and so on. Binding kinetic experiments demonstrated that the 2D imprinting approach can improve site accessibility for the template effectively. The 2D MIM exhibited binding affinity and specificity for the template, as revealed by equilibrium binding experiments. When using MIM as a stationary phase for HPLC, baseline separation of cholesterol from other compounds can be achieved. In addition, the use of 2D imprinting significantly reduced the peak broadening and tailing.

Journal ArticleDOI
TL;DR: A motion boundary based sampling strategy and spatial-temporal co-occurrence descriptors for action video representation and recognition and the results show that the sampling strategy significantly reduces the computational cost of point tracking without degrading performance.

Journal ArticleDOI
TL;DR: A comprehensive review of the literature on memory impairment and the potential effective factors in patients with chronic pain and the currently available data and theory have explained memory impairment in chronic pain patients, but many controversies remain.
Abstract: Objective This study provides a comprehensive review of the literature on memory impairment and the potential effective factors in patients with chronic pain. Methods A literature search of databases PubMed, EMBASE, SpringerLink, and PsycINFO until September 2012 was conducted using the keywords ‘memory’ and ‘chronic pain’. The study emphasises on publications over the past 20 years. Results Memory impairment in chronic pain patients is substantial, but the aspects of memory (e.g. working memory, long-term memory, and autobiographical memory) in chronic pain patients and the potentially related factors (e.g. age, level of education, pain conditions, emotion, neural network, and use of analgesics) are modest. Memory impairment is interpreted with the attention-narrowing hypothesis and the capacity-reduction hypothesis. Conclusions The currently available data and theory have explained memory impairment in chronic pain patients, but many controversies remain. Future research should focus on the subclinical characteristics of chronic pain, enlarging the sample size, and emphasise on the experimental intervention method and the cognitive neuroscience method.

Journal ArticleDOI
TL;DR: The retrieval of AM in patients with chronic pain tends to be overgeneral and delayed, and the retrieval style of AM may be contributed to negative emotions and chronic pain conditions.
Abstract: Objective Overgenerality and delay of the retrieval of autobiographical memory (AM) are well documented in a range of clinical conditions, particularly in patients with emotional disorder. The present study extended the investigation to chronic pain, attempting to identify whether the retrieval of AM in patients with chronic pain tends to be overgeneral or delayed. Design With an observational cross-sectional design, we evaluated the AM both in patients with chronic pain and healthy controls by Autobiographical Memory Test. Pain conditions were assessed using the pain diagnostic protocol, the short-form McGill Pain Questionnaire (SF-MPQ), and the Pain Self-Efficacy Questionnaire (PSEQ). Emotion was assessed using the Beck Depression Inventory-II (BDI-II) and the Beck Anxiety Inventory. Subjects and Settings Subjects included 176 outpatients with chronic pain lasting for at least 6 months and 170 healthy controls. Results 1) Compared with the healthy group, the chronic pain group had more overgeneral memories (OGMs) (F = 29.061, P < 0.01) and longer latency (F = 13.602, P < 0.01). 2) In the chronic pain group, the stepwise multiple regression models for variables predicting OGM were significant (P < 0.01). Specifically, the variance in OGM scores could be predicted by the BDI score (9.7%), pain chronicity (4.3%), PSEQ score (7.1%), and Affective Index (of SF-MPQ) score (2.7%). 3) In the chronic pain group, the stepwise multiple regression models for variables predicting latency were significant (P < 0.05). Specifically, the variance in latency could be predicted by age (3.1%), pain chronicity (2.7%), pain duration (4.3%), and PSEQ score (2.0%). Conclusions The retrieval of AM in patients with chronic pain tends to be overgeneral and delayed, and the retrieval style of AM may be contributed to negative emotions and chronic pain conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the properties of solutions f to the nonhomogenous Yukawa equation Δf(z) = λ(z), where λ is a real function from $$\mathbb{B}^n$$cffff into ℝ, and showed that the main result of Girela, Pavlovic and Pelaez on analytic functions can be extended to this more general setting.
Abstract: In this paper, we investigate some properties of solutions f to the nonhomogenous Yukawa equation Δf(z) = λ(z)f(z) in the unit ball $$\mathbb{B}^n$$ of ℂ n , where λ is a real function from $$\mathbb{B}^n$$ into ℝ. First, we prove that a main result of Girela, Pavlovic and Pelaez (J. Analyse Math. 100 (2006), 53–81) on analytic functions can be extended to this more general setting. Then we study relationships on such solutions between the bounded mean oscillation and Lipschitz-type spaces. The obtained result generalized the corresponding result of Dyakonov (Acta Math. 178 (1997), 143–167). Finally, we discuss Dirichlet-type energy integrals on such solutions in the unit ball of ℂ n and give an application.

Journal ArticleDOI
TL;DR: In this article, the authors give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk, and generalize results of Colonna for planar harmonic mappings in (Indiana Univ. Math. 38: 829-840, 1989).
Abstract: In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic mappings in (Indiana Univ. Math. J. 38: 829-840, 1989).

Journal ArticleDOI
TL;DR: In this article, the authors studied the complete convergence results for Sung's type weighted sums of sequences of end random variables and obtained some new results, which extend and improve the corresponding theorems of Sung.
Abstract: In this paper, the author studies the complete convergence results for Sung’s type weighted sums of sequences of END random variables and obtains some new results. These results extend and improve the corresponding theorems of Sung (Discrete Dyn. Nat. Soc. 2010:630608, 2010, doi:10.1155/2010/630608).

Journal ArticleDOI
TL;DR: In this article, the adsorption kinetics, isotherms, and effects of various parameters, such as temperature, contact time, solution pH, adsorbent dosage, and initial U(VI) concentration on the UVI removal process were studied.
Abstract: Activated palm kernel shell carbon (APKSC) was used to remove U(VI) from aqueous solutions in a batch system. The adsorption kinetics, isotherms, and effects of various parameters, such as temperature, contact time, solution pH, adsorbent dosage, and initial U(VI) concentration on the U(VI) adsorption process were studied. Equilibrium was reached after 120 min in the range of studied U(VI) concentrations and temperatures. U(VI) uptake was insignificantly affected by temperature, but was highly pH dependent, and the optimum pH for removal was 5.5. U(VI) removal efficiency increased with the increasing adsorbent dosage. U(VI) sorption capacity increased with increasing initial U(VI) concentration; any further increases in initial U(VI) concentration above a certain point caused insignificant changes in U(VI) sorption capacity. Isotherm data could be described by the Langmuir isotherm model with a maximum U(VI) adsorption capacity of 51.81 mg/g. Kinetic data were fitted to pseudo-first-order and pseudo-second-order equations, which suggested that the U(VI) adsorption onto APKSC was better reproduced by the pseudo-second-order model rather than pseudo-first-order model. Our results indicated that APKSC might be used as a cheap adsorbent in the treatment of uranium-containing wastewater.

Journal ArticleDOI
TL;DR: In this paper, the spin-dependent splitting in intrinsic photonic spin Hall effect has been investigated and shown to be tunable by breaking the rotational symmetry of a cylindrical vector beam.
Abstract: We report the realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect. By breaking the rotational symmetry of a cylindrical vector beam, the intrinsic vortex phases that the two spin components of the vector beam carries, which is similar to the geometric Pancharatnam-Berry phase, is no longer continuous in the azimuthal direction, and leads to observation of spin accumulation at the opposite edge of the beam. Due to the inherent nature of the phase and independency of light-matter interaction, the observed photonic spin Hall effect is intrinsic. Modulating the topological charge of the vector beam, the spin-dependent splitting can be enhanced and the direction of spin accumulation is switchable. Our findings may provide a possible route for generation and manipulation of spin-polarized photons, and enables spin-based photonics applications.

Posted Content
TL;DR: In this article, the authors give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk, which are generalizations of results of Colonna for planar harmonic mappings in [Indiana Univ. Math. 38: 829--840, 1989].
Abstract: In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic mappings in [Indiana Univ. Math. J. 38: 829--840, 1989].

Journal ArticleDOI
01 Jan 2014-Optik
TL;DR: A simplified ray tracing method for optical MIMO system to obtain its channel impulse response and frequency response is presented and its validity is verified by the numerical simulations.

Journal ArticleDOI
TL;DR: By applying nonequilibrium Green's functions in combination with density-function theory, this article investigated the spin-dependent transport properties of graphene and boron nitride nanoribbon heterostructure decorated with chromium-ligand.

Journal ArticleDOI
TL;DR: The new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework based on the positive homogenous and concave/convex measures of reward and risk, respectively.
Abstract: In this article, we study reward–risk ratio models under partially known message of random variables, which is called robust (worst-case) performance ratio problem. Based on the positive homogenous and concave/convex measures of reward and risk, respectively, the new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework. Under some specially partial distribution situation, the convex optimization problem is converted into simple framework involving the expectation reward measure and conditional value-at-risk measure. Compared with the existing reward–risk portfolio research, the proposed ratio model has two characteristics. First, the addressed problem combines with two different aspects. One is to consider an incomplete information case in real-life uncertainty. The other is to focus on the performance ratio optimization problem, which can realize the best balance between the reward and risk. Second, the complicated optimization model is transfer...

Journal ArticleDOI
TL;DR: The present study provides a new kind of composite material which contains moveable and flexible grippers for recognizing and binding guest molecules and displayed affinity binding ability for saccharides under physiological pH value and allowed saccharide-sensitive material to be conveniently separated from solution.

Journal ArticleDOI
TL;DR: Based on ab initio density functional theory calculations within the generalized gradient approximation, the electronic structure and magnetic properties of the one and two-C-doped CdS monolayer are investigated in this article.
Abstract: Based on ab initio density functional theory calculations within the generalized gradient approximation, the electronic structure and magnetic properties of the one- and two-C-doped CdS monolayer are investigated. The results show that the C-doped CdS system exhibits half-metallic behaviors with a total magnetic moment of 2.0μB/C, which is in good accord with the results obtained from the HSE06 functional. The magnetic moment mainly comes from the spin-polarized C-2p states in the band gap. The long-range ferromagnetic order with a Curie temperature of about 280 K is attributed to the p–d and p–p hybridizations via the C–Cd–S coupling chains.

Journal ArticleDOI
TL;DR: The improved algorithm can improve the performance in terms of peak signal to noise ratio (PSNR) of solder joint imagery recovery and could achieve the best results on PSNR when compared to other methods such as the orthogonal matching pursuit algorithm, greedy basis pursuit algorithms, subspace pursuit algorithm and compressive sampling matching pursuit algorithms.
Abstract: Purpose – The purpose of this paper is to develop an improved compressive sensing algorithm for solder joint imagery compressing and recovery. The improved algorithm can improve the performance in terms of peak signal to noise ratio (PSNR) of solder joint imagery recovery. Design/methodology/approach – Unlike the traditional method, at first, the image was transformed into a sparse signal by discrete cosine transform; then the solder joint image was divided into blocks, and each image block was transformed into a one-dimensional data vector. At last, a block compressive sampling matching pursuit was proposed, and the proposed algorithm with different block sizes was used in recovering the solder joint imagery. Findings – The experiments showed that the proposed algorithm could achieve the best results on PSNR when compared to other methods such as the orthogonal matching pursuit algorithm, greedy basis pursuit algorithm, subspace pursuit algorithm and compressive sampling matching pursuit algorithm. When ...

Journal ArticleDOI
TL;DR: In this paper, the propagation properties of anomalous hollow beams in strongly isotropic nonlocal media are investigated based on the nonlocal nonlinear Schrodinger equation, and the analytical expressions of the beam propagation, the on-axis intensity and the beam width are obtained.
Abstract: Based on the nonlocal nonlinear Schrodinger equation, the propagation properties of anomalous hollow beams in strongly isotropic nonlocal media are investigated. The analytical expressions of the beam propagation, the on-axis intensity and the beam width are obtained. The results show that the evolution of the beam is periodical and the input power is the most important parameter. The input power determines the variation of the period. Furthermore, it is found that there exists a critical input power in the x direction and in the y direction separately when the initial beam widths in the two transversal directions are unequal. The beam width remains invariant in the corresponding transversal direction when the input power equals the critical power in one of the transversal directions. Selecting a proper input power, the beam can be broadened or compressed in the two transversal directions at the same time. In particular, the beam can be broadened (compressed) in one transversal direction, whereas in the other transversal direction, it is compressed (broadened), i.e., the transversal reverse transformation.