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It is shown that the nonlinear pendulum equation can be transformed into a linear harmonic oscillator in the phase space thanks to Kerner’s method [12]. Moreover, as a mathematical divertissement, the second-order differential equation determining the phase-space trajectories of the nonlinear pendulum is quantized.

It is shown that the nonlinear pendulum equation can be transformed into a linear harmonic oscillator in the phase space thanks to Kerner’s method [12]. Moreover, as a mathematical divertissement, the second-order differential equation determining the phase-space trajectories of the nonlinear pendulum is quantized.

The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M. C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. The result is different from that given in [K. Kowalski, J. Rembielński, Ann. Phys. 329 (2013) 146]. A comparison of the different outcomes is provided.

The prognostic factors and optimal therapy for invasive pulmonary aspergillosis (IPA) after kidney transplantation (KT) remain poorly studied. We included in this multinational retrospective study 112 recipients diagnosed with probable (75.0% of cases) or proven (25.0%) IPAbetween 2000 and 2013. The median interval from transplantation to diagnosis was 230 days. Cough, fever, and expectoration were the most common symptoms at presentation. Bilateral pulmonary involvement was observed in 63.6% of cases. Positivity rates for the galactomannan assay in serum and bronchoalveolar lavage samples were 61.3% and 57.1%, respectively. Aspergillus fumigatuswas the most commonly identified species. Six‐ and 12‐week survival rates were 68.8% and 60.7%, respectively, and 22.1% of survivors experienced graft loss. Occurrence of IPAwithin the first 6 months (hazard ratio [HR]: 2.29; p‐value = 0.027) and bilateral involvement at diagnosis (HR: 3.00; p‐value = 0.017) were independent predictors for 6‐week all‐cause mortality, whereas the initial use of a voriconazole‐based regimen showed a protective effect (HR: 0.34; p‐value = 0.007). The administration of antifungal combination therapy had no apparent impact on outcome. In conclusion, IPAentails a dismal prognosis among KTrecipients. Maintaining a low clinical suspicion threshold is key to achieve a prompt diagnosis and to initiate voriconazole therapy. Invasive pulmonary aspergillosis presents a high mortality rate in kidney transplant recipients, with diagnosis within the first 6 months posttransplantation and bilateral lung involvement as independent risk factors for mortality.

The prognostic factors and optimal therapy for invasive pulmonary aspergillosis (IPA) after kidney transplantation (KT) remain poorly studied. We included in this multinational retrospective study 112 recipients diagnosed with probable (75.0% of cases) or proven (25.0%) IPA between 2000 and 2013. The median interval from transplantation to diagnosis was 230 days. Cough, fever, and expectoration were the most common symptoms at presentation. Bilateral pulmonary involvement was observed in 63.6% of cases. Positivity rates for the galactomannan assay in serum and bronchoalveolar lavage samples were 61.3% and 57.1%, respectively. Aspergillus fumigatuswas the most commonly identified species. Six- and 12-week survival rates were 68.8% and 60.7%, respectively, and 22.1% of survivors experienced graft loss. Occurrence of IPA within the first 6 months (hazard ratio [HR]: 2.29; p-value = 0.027) and bilateral involvement at diagnosis (HR: 3.00; p-value = 0.017) were independent predictors for 6-week all-cause mortality, whereas the initial use of a voriconazole-based regimen showed a protective effect (HR: 0.34; p-value = 0.007). The administration of antifungal combination therapy had no apparent impact on outcome. In conclusion, IPA entails a dismal prognosis among KT recipients. Maintaining a low clinical suspicion threshold is key to achieve a prompt diagnosis and to initiate voriconazole therapy.

Risk factors for invasive pulmonary aspergillosis (IPA) after kidney transplantation have been poorly explored. We performed a multinational case–control study that included 51 kidney transplant (KT)recipients diagnosed with early (first 180 posttransplant days) IPAat 19 institutions between 2000 and 2013. Control recipients were matched (1:1 ratio) by center and date of transplantation. Overall mortality among cases was 60.8%, and 25.0% of living recipients experienced graft loss. Pretransplant diagnosis of chronic pulmonary obstructive disease (COPD; odds ratio [OR]: 9.96; 95% confidence interval [CI]: 1.09–90.58; p = 0.041) and delayed graft function (OR: 3.40; 95% CI: 1.08–10.73; p = 0.037) were identified as independent risk factors for IPAamong those variables already available in the immediate peritransplant period. The development of bloodstream infection (OR: 18.76; 95% CI: 1.04–339.37; p = 0.047) and acute graft rejection (OR: 40.73, 95% CI: 3.63–456.98; p = 0.003) within the 3 mo prior to the diagnosis of IPAacted as risk factors during the subsequent period. In conclusion, pretransplant COPD, impaired graft function and the occurrence of serious posttransplant infections may be useful to identify KTrecipients at the highest risk of early IPA. Future studies should explore the potential benefit of antimold prophylaxis in this group. A multinational case‐control study in kidney transplant recipients finds that pretransplant diagnosis of chronic obstructive pulmonary disease, delayed graft function, bloodstream infection and acute graft rejection identify patients at the highest risk for early invasive pulmonary aspergillosis.

Risk factors for invasive pulmonary aspergillosis (IPA) after kidney transplantation have been poorly explored. We performed a multinational case–control study that included 51 kidney transplant (KT) recipients diagnosed with early (first 180 posttransplant days) IPA at 19 institutions between 2000 and 2013. Control recipients were matched (1:1 ratio) by center and date of transplantation. Overall mortality among cases was 60.8%, and 25.0% of living recipients experienced graft loss. Pretransplant diagnosis of chronic pulmonary obstructive disease (COPD; odds ratio [OR]: 9.96; 95% confidence interval [CI]: 1.09–90.58; p = 0.041) and delayed graft function (OR: 3.40; 95% CI: 1.08–10.73; p = 0.037) were identified as independent risk factors for IPA among those variables already available in the immediate peritransplant period. The development of bloodstream infection (OR: 18.76; 95% CI: 1.04–339.37; p = 0.047) and acute graft rejection (OR: 40.73, 95% CI: 3.63–456.98; p = 0.003) within the 3 mo prior to the diagnosis of IPA acted as risk factors during the subsequent period. In conclusion, pretransplant COPD, impaired graft function and the occurrence of serious posttransplant infections may be useful to identify KT recipients at the highest risk of early IPA. Future studies should explore the potential benefit of antimold prophylaxis in this group.

The classical quantization of a Liénard-type nonlinear oscillator is achieved by a quantization scheme (M. C. Nucci. Theor. Math. Phys., 168:994–1001, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation in the momentum space as given in (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light on the apparently remarkable connection with the linear harmonic oscillator.

The nonclassical symmetries method is applied to a class of reaction-diffusion equations with nonlinear source, i.e. ut= uxx+ cux+ R(u,x). Several cases are obtained by using suitable solutions of the heir-equations as described in [M.C. Nucci, Nonclassical symmetries as special solutions of heir-equations, J. Math. Anal. Appl.279(2003) 168–179].

In this Letter a first-order Lagrangian for the Schrödinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D56(8) (1997) 4844–4877]. Then Noether's theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schrödinger–Newton equations, Nonlinearity19(7) (2006) 1507–1514] in order to find conservation laws of the Schrödinger–Newton equations.

We show that a method presented in [S. L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol.48(1974) 299–324] and later in [G. H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol.44(1982) 749–760] for finding Lagrangians of classic models in biology, is actually based on finding the Jacobi Last Multiplier of such models. Using known properties of Jacobi Last Multiplier we show how to obtain linear Lagrangians of systems of two first-order ordinary differential equations and nonlinear Lagrangian of the corresponding single second-order equation that can be derived from them, even in the case where those authors failed such as the host-parasite model. Also we show that the Lagrangians of certain second-order ordinary differential equations derived by Volterra in [V. Volterra, Calculus of variations and the logistic curve, Hum. Biol.11(1939) 173–178] are particular cases of the Lagrangians that can be obtained by means of the Jacobi Last Multiplier. Actually we provide more than one Lagrangian for those Volterra's equations.

We show that a method presented in [S. L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol.48(1974) 299–324] and later in [G. H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol.44(1982) 749–760] for finding Lagrangians of classic models in biology, is actually based on finding the Jacobi Last Multiplier of such models. Using known properties of Jacobi Last Multiplier we show how to obtain linear Lagrangians of systems of two first-order ordinary differential equations and nonlinear Lagrangian of the corresponding single second-order equation that can be derived from them, even in the case where those authors failed such as the host-parasite model. Also we show that the Lagrangians of certain second-order ordinary differential equations derived by Volterra in [V. Volterra, Calculus of variations and the logistic curve, Hum. Biol.11(1939) 173–178] are particular cases of the Lagrangians that can be obtained by means of the Jacobi Last Multiplier. Actually we provide more than one Lagrangian for those Volterra’s equations.

In this Letter a first-order Lagrangian for the Schrödinger—Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D56(8) (1997) 4844–4877]. Then Noether’s theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schrödinger—Newton equations, Nonlinearity19(7) (2006) 1507–1514] in order to find conservation laws of the Schrödinger—Newton equations.

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations, including a class of equations recently studied by Musielak with his own method [Z. E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients J. Phys. A: Math. Theor.41(2008) 055205], and in particular a Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.

We present an equation of the fourth-order which does not possess a second-order Lagrangian and demonstrate by means of the method of reduction of order that one can obtain a first-order Lagrangian for it. This opens the way to quantization through the construction of an Hamiltonian which is suitable to be quantized according to the procedure of Dirac with the correct physical attributes.

We present an equation of the fourth-order which does not possess a second-order Lagrangian and demonstrate by means of the method of reduction of order that one can obtain a first-order Lagrangian for it. This opens the way to quantization through the construction of an Hamiltonian which is suitable to be quantized according to the procedure of Dirac with the correct physical attributes.

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi’s method by applying it to several equations, including a class of equations recently studied by Musielak with his own method [Z. E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients J. Phys. A: Math. Theor.41(2008) 055205], and in particular a Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations, including a class of equations recently studied by Musielak with his own method [Z. E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients J. Phys. A: Math. Theor.41(2008) 055205], and in particular a Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.

In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi's method.

We apply the method of Jacobi Last Multiplier to the fifty second-order ordinary differential equations of Painlevé type as given in Ince in order to obtain a Lagrangian and consequently solve the inverse problem of Calculus of Variations for those equations. The easiness and straightforwardness of Jacobi's method is underlined.

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and η-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.

We apply the method of Jacobi Last Multiplier to the fifty second-order ordinary differential equations of Painlevé type as given in Ince in order to obtain a Lagrangian and consequently solve the inverse problem of Calculus of Variations for those equations. The easiness and straightforwardness of Jacobi's method is underlined.

In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi's method.

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and η-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.

We apply the method of Jacobi Last Multiplier to the fifty second-order ordinary differential equations of Painlevé type as given in Ince in order to obtain a Lagrangian and consequently solve the inverse problem of Calculus of Variations for those equations. The easiness and straightforwardness of Jacobi’s method is underlined.

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and η-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.

In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi’s method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi’s method.

We use a method inspired by the Jacobi last multiplier [M.C. Nucci, Jacobi last multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear Math. Phys. 12, 284–304 (2005)] in order to find Lie symmetries of a Painlevé-type equation without Lie point symmetries.

We apply singularity analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng (J Math Biol35(1997) 629–656) for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-Hernández (J Math Biol35(1997) 523–544) to identify values of the parameters for which the system of nonlinear first-order ordinary differential equations describing the model are integrable. A number of combinations of parameters for which the system is integrable are identified. We compare them with the results we obtained by a symmetry analysis in an earlier paper (J Math Anal Appl333(2007) 430–449.

AbstractWe use a method inspired by the Jacobi last multiplier [M.C. Nucci, Jacobi last multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear Math. Phys. 12, 284–304 (2005)] in order to find Lie symmetries of a Painlevé-type equation without Lie point symmetries.

Lie group analysis is applied to a core group model for sexually transmitted disease formulated by Hadeler and Castillo-Chavez [Hadeler K P and Castillo-Chavez C, A core group model for disease transmission, Math. Biosci.128(1995), 41–55]. Several instances of integrability even linearity are found which lead to the general solution of the model. A discussion of such solutions is presented and it is shown how they complement Hadeler and Castillo-Chavez’s qualitative analysis.

In [18] Jacobi introduced a third-order nonlinear ordinary differential equation which links two different moduli of an elliptic integral. In the present paper Lie group analysis is applied to that equation named Jacobi’s modular differential equation. A six-dimensional Lie symmetry algebra is obtained and its symmetry generators are found to be given in terms of elliptic integrals. As a consequence the transformation between Jacobi’s modular differential equation and the well-known Schwarzian differential equation is derived.

The Ermakov-Pinney equation possesses three Lie point symmetries with the algebra sl(2, R). This algebra does not provide a representation of the complete symmetry group of the Ermakov-Pinney equation. We show how the representation of the group can be obtained with the use of the method described in Nucci, J. Nonlin. Math. Phys.12(2005) (this issue), which is based on the properties of Jacobi’s last multiplier (Bianchi L, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, Enrico Spoerri, Pisa, 1918), the method of reduction of order (Nucci, J. Math. Phys37(1996), 1772–1775) and an interactive code for calculating symmetries (Nucci, Interactive REDUCE programs for calcuating classical, non-classical and Lie-Bäcklund symmetries for differential equations (preprint: Georgia Institute of Technology, Math 062090-051, 1990, and CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 3: New Trends in Theoretical Developments and Computational Methods, Editor: Ibragimov N H, CRC Press, Boca Raton, 1996, 415–481).

After giving a brief account of the Jacobi last multiplier for ordinary differential equations and its known relationship with Lie symmetries, we present a novel application which exploits the Jacobi last multiplier to the purpose of finding Lie symmetries of first-order systems. Several illustrative examples are given.

The problem of three bodies which attract each other with forces proportional to the cube of the inverse of their distance and move on a line was reduced to one quadrature by Jacobi [23]. Here we show that the equations of motions admit a five-dimensional Lie symmetry algebra and can be reduced to a single second-order linear equation, i.e. the equation of motion of a single free particle on the line.

AbstractThe symmetry approach to the determination of Jacobi’s last multiplier is inverted to provide a source of additional symmetries for the Euler–Poinsot system. These additional symmetries are nonlocal. They provide the symmetries for the representation of the complete symmetry group of the system.

AbstractRealizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.

The symmetry approach to the determination of Jacobi’s last multiplier is inverted to provide a source of additional symmetries for the Euler—Poinsot system. These additional symmetries are nonlocal. They provide the symmetries for the representation of the complete symmetry group of the system.

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.

AbstractWe show that the concept of complete symmetry group introduced by Krause (J. Math. Phys.35(1994), 5734–5748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations describing spherically symmetric bodies with certain conformal Killing symmetries. We also provide a simple demonstration of the nonuniqueness of the complete symmetry group.

We show that the concept of complete symmetry group introduced by Krause (J. Math. Phys. 35(1994), 5734–5748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations describing spherically symmetric bodies with certain conformal Killing symmetries. We also provide a simple demonstration of the nonuniqueness of the complete symmetry group.

Two fungal isolates recovered from the blood of two immunosuppressed patients are described as Phialemonium curvatum. One patient died, while the other, who was infected with Exophiala jeanselmei at the same time, survived after successful treatment with itraconazole. Analysis of internal transcribed spacer sequences demonstrated that the isolates belonged to the same strain and that the source of infection was probably a catheter. The taxonomic position of P. curvatum is discussed, and Phialemonium dimorphosporum is considered a synonym. The in vitro inhibitory activities of six antifungal agents (amphotericin B, itraconazole, ketaconazole, miconazole, flucytosine, and fluconazole) were determined against seven isolates of Phialemonium. Except for flucytosine, all of them were remarkably effective. Phialemonium should be added to the list of potential causes of nosocomial fungemia in cancer patients.

Sommario Si fa l'analisi gruppale completa dell'equazione del seconda ordine che governa le deformazioni di un mezzo iperelastico omogeneo ed isotropo. Si caratterizzano alcune soluzioni esatte di similaritá che corrispondono a classi di materiali compatibili con le condizioni di invarianza. Si studia la propagazione di onde sferiche di discontinuitá in uno stato non costante caratterizzato dalle soluzioni suddette.

A prospective randomized trial was performed to compare the efficacy of a regimen containing a glycopeptide versus one containing a beta-lactamase inhibitor in the treatment of febrile episodes in neutropenic patients. Fifty-eight patients received piperacillin/amikacin/teicoplanin (group 1) and 56 received piperacillin/amikacin/tazobactam (group 2). In the case of persistence of fever without microbiological documentation of the cause, teicoplanin was also given empirically in group 2 on day 4, and amphotericin B in both groups on day 6. In 114 evaluable febrile episodes, the rate of success without modification of therapy was 60 % in patients on piperacillin/amikacin/teicoplanin and 41 % in patients on piperacillin/amikacin/tazobactam (p<0.03). Eleven of 34 patients in the latter group who failed to improve eventually responded upon addition of teicoplanin. Ten and nine patients in group 1 and group 2 respectively required the addition of amphotericin B for definite improvement. There were 14 episodes of gram-positive septicemia in each group: the response rate was 100 % in group 1 and 43 % in group 2. Three episodes of gram-negative breakthrough septicemia occurred in group 1 versus no cases in group 2 (p=0.1). Three deaths occurred in each group. Piperacillin/amikacin/tazobactam may be as efficacious as piperacillin/amikacin/teicoplanin in the treatment of febrile neutropenic patients provided the regimen is modified (usually by addition of teicoplanin) in unresponsive cases.

A hierarchy of nonlinear evolution equations based on the IKW nonlinear oscillation equation is shown to be invariant under a reciprocal Bäcklund transformation. This result is seen to be a consequence of a simple invariance of the modified Korteweg-deVries hierarchy.