V. I. Shenavrin

• Lomonosov Moscow State University

The results of photometric and spectral observations of T CrB obtained in a wide range of wavelengths in 2011–2023 are presented. We use the near-IR light curves to determine a new ephemeris JDmin=2455828,9+227,55E for the times of light minima when the red giant is located between the observer and the hot component. The flux ratio Ha/Hb varied fro...

We present the results of a new stage of the long-term photometric study of FG Sge which is a quickly evolving central star of the planetary nebula Hen 1-5. Our new observations carried out on the SAI MSU telescopes in the optical ($BVR_CI_C$) and infrared (IR) ($JHKLM$) regions in 2008-2021 and 2013-2021, respectively, allowed us to trace the evol...

The long-period, highly eccentric Wolf-Rayet star binary system WR 140 has exceptionally well-determined orbital and stellar parameters. Bright, variable X-ray emission is generated in shocks produced by the collision of the winds of the WC7pd+O5.5fc component stars. We discuss the variations in the context of the colliding-wind model using broadba...

WR 140 is a long-period, highly eccentric Wolf-Rayet star binary system with exceptionally well-determined orbital and stellar parameters. Bright, variable X-ray emission is generated in shocks produced by the collision of the winds of the WC7pd+O5.5fc component stars. We discuss the variations in the context of the colliding-wind model using broad...

The star V426 Sge (HBHA~1704-05), originally classified as an emission-line object and a semi-regular variable, brightened at the beginning of August 2018, showing signatures of a symbiotic star outburst. We aim to confirm the nature of V426 Sge as a classical symbiotic star, determine the photometric ephemeris of the light minima, and suggest the...

Context. The star V426 Sge (HBHA 1704-05), originally classified as an emission-line object and a semi-regular variable, brightened at the beginning of August 2018, showing signatures of a symbiotic star outburst. Aims. We aim to confirm the nature of V426 Sge as a classical symbiotic star, determine the photometric ephemeris of the light minima, a...

We present the results of a new epoch of a long-term photometric monitoring of the variable planetary nebula IC~4997. The integral $UBV$ light curves display a continuing brightening of 0.$^{m}15$ in $V$, a slight rise (<0.$^{m}1$) in $B$, and constancy in $U$. The $B-V$ color has got redder from 0.$^{m}4$ in 2000 to 0.$^{m}7$ in 2019, whereas the...

The results of many-year infrared observations of the Herbig AeBe star AB Aur at 1-5 μm (JHKLM bands) are presented. The duration of the photometric series, together with observations published earlier, is about 18 years. The observations demonstrate that, in contrast to the optical, the star is quite active in the studied infrared range. The varia...

Temporal variation of millimeter lines is a new direction of research for evolved stars. It has the potential to probe the dynamical wind-launching processes from a time dimension. We report here the first Atacama Large Millimeter Array (ALMA) results that cover 817 days of ongoing monitoring of 1.1 mm lines in the archetypal carbon star IRC +10216...

We present results of a study of the correlation between the infrared (JHKL) and optical(B) fluxes of the nucleus of the Seyfert galaxy NGC 4151 for the years 2010 - 2015 using our own data (partially published) in combination with published data of Roberts and Rumstey (2012), Guo et al. (2014) and Schnulle et al. (2013, 2015).We find similar lags...

Based on the multiband (BVRIJHKL) photometric observations of the active red giant PZ Mon performed for the first time in the winter season of 2017-2018, we have determined the main characteristics of the spotted stellar surface in a parametric three-spot model. The unspotted surface temperature is Teff=4730 K, the temperature of the cool spots is...

Temporal variation of millimeter lines is a new direction of research for evolved stars. It has the potential to probe the dynamical wind launching processes from time dimension. We report here the first results that cover the past 817 days of an on-going monitoring project for 1.1\,mm lines in the archetypal carbon star IRC\,+10216, using both the...

We present results of a study of the correlation between the infrared (JHKL) and optical (B) fluxes of the nucleus of the Seyfert galaxy NGC 4151 for the years 2010–2015 using our own data (partially published) in combination with published data of Roberts and Rumstey (2012), Guo et al. (2014) and Schnülle et al. (2013, 2015). We find similar lags...

Classical T Tauri stars with ages of less than 10 Myr possess accretion discs. Magnetohydrodynamic processes at the boundary between the disc and the stellar magnetosphere control the accretion and ejections gas flows. We carried out a long series of simultaneous spectroscopic and photometric observations of the classical T Tauri stars, RY Tauri an...

The results of UBVRIJHKLM photometry and VRI polarimetry of a young star RW Aur A observed during unprecedented long and deep (up to V ≈ 5 mag) dimming events in 2010–11 and 2014–18 are presented. The polarization degree p of RW Aur A at this period has reached 30 per cent in the I band. As in the case of UX Ori-type stars (UXORs), the so-called ‘b...

We present the results of our photometric UBV JHKL observations for the symbiotic star V1413 Aql obtained in 2012–2018. An analysis of the data has shown that inMay 2017 the system passed to a quiescent state with B − V ≈ 0ṃ 6 for the first time since 1993. It lasted no more than five months. The J − K color at the primary minimum of 2012 reached 1...

Classical T Tauri stars with ages of less than 10 Myr possess accretion discs. Magnetohydrodynamic processes at the boundary between the disc and the stellar magnetosphere control the accretion and ejections gas flows. We carried out a long series of simultaneous spectroscopic and photometric observations of the classical T Tauri stars RY Tau and S...

Results of $UBVRIJHKLM$ photometry and $VRI$ polarimetry of a young star RW Aur A observed during unprecedented long and deep (up to $\Delta V \approx 5$ mag) dimming events in 2010-11 and 2014-18 are presented. The polarization degree $p$ of RW Aur A at this period has reached 30 per cent in the $I$ band. As in the case of UX Ori type stars (UXORs...

We present results of a study of the correlation between the infrared (JHKL) and optical (B) fluxes of the nucleus of the Seyfert galaxy NGC 4151 for the years 2010–2015 using our own data (partially published) in combination with published data [1, 2, 3, 4]. We find similar lags for each of the HKL passbands relative to the optical of 37 ± 3 days. T...

In three seasons of 2015-2018 we carried out a series of visible and near infrared (NIR) photometry of SU Aur. In course of this photometric monitoring we detected an event of a deep fading of the star in spring of 2018. In this paper we present preliminary analysis of our photometry.

We present the results of multicolor (UBV JHKLM) photometry (2009–2017) and low-resolution spectroscopy (2016–2017) of the semi-regular variable V1427 Aql = HD 179821, a yellow supergiant with gas-dust envelope. The star displays low-amplitude (ΔV<0 m. 2) semi-periodic brightness variations superimposed on a long-term trend. The light curve shape a...

We present the results of multicolor (UBVJHKLM) photometry (2009-2017) and low-resolution spectroscopy (2016-2017) of the semi-regular variable V1427 Aql=HD 179821, a yellow supergiant with gas-dust envelope. The star displays low-amplitude ({\Delta}V<0.2 mag) semi-periodic brightness variation superimposed on a long-term trend. The light curve sha...

A new set of low-resolution spectral and UBVJHKL-photometric observations of the symbiotic nova PU Vul is presented. The binary has been still evolving after the symbiotic nova outburst in 1977 and now it's in the nebular stage. It is found that the third orbital cycle (after 1977) was characterized by great changes in light curves. Now PU Vul demo...

A new set of low-resolution spectral and UBVJHKL-photometric observations of the symbiotic nova PU Vul is presented. The binary has been still evolving after the symbiotic nova outburst in 1977 and now it's in the nebular stage. It is found that the third orbital cycle (after 1977) was characterized by great changes in light curves. Now PU Vul demo...

The results of infrared observations of the two Be stars X Per and V725 Tau, which are the optical components of X-ray binary systems, obtained in 1994–2016 are presented. The observations cover Be-star phases as well as shell phases. The data analysis shows that the radiation observed from the binaries at 1.25, 3.5, and 5 μm can be explained as th...

We present the results of JHKLM-photometry for the symbiotic Mira star candidate V 335 Vul. Based on the average flux data, supplemented by IRAS, MSX, AKARI, and WISE mid-IR observations, we calculated a model of a spherically symmetric dust envelope of the star, made up of amorphous carbon and silicon carbide particles. The optical depth of the en...

Results of UBVRIJHKLM photometry, VRI polarimetry and optical spectroscopy of a young star RW Aur A obtained during 2010-11 and 2014-16 dimming events are presented. During the second dimming the star decreased its brightness to \Delta V > 4.5 mag, polarization of its light in I-band was up to 30%, and color-magnitude diagram was similar to that of...

We analyze the results of our spectroscopic monitoring of V407 Cyg in 2001--2009. The slow decline in optical brightness connected with the evolution of a Z And-type outburst (maximum in 1998) was observed in 2001--2003. The system returned to quiescence in 2004, and its spectrum returned to nearly the same as in 1994. We estimated the hot componen...

We present UBVJHKLM photometric observations of Nova Delphini 2013 that started several hours before maximum light and lasted for 130 nights. Using the obtained data, we derived several photometric parameters of the Nova: the time of maximum light, brightness at maximum, rate of decline, t(2) = 11 d. This places Nova Del 2013 among fast novae accor...

We present the results of our

We present the results of our long-term UBV JHKLM photometry and spectroscopic monitoring of the symbiotic nova V1016 Cyg. After its outburst in 1964, the star showed fading in the U, B, V bands at a rate of about 0.03 mag per year. The behavior of the B − V and U − B color indices reflects variations of the emission lines, fading of the erupted co...

The results of ~15 years of photometric observations of the UX Ori star SV Cep in the near-infrared (JHKL) are presented. They demonstrate the presence of a cyclic component with a period of ~7 years in the variations of the IR fluxes. This is clearly seen in all four IR bands, but is absent in the optical. The variation amplitude is highest in the...

We present the results of our UBV and JHKLM photometry for the semiregular pulsating variable V1027 Cyg, a supergiant with an infrared excess, over the period from 1997 to 2015 (UBV) and in 2009–2015 (JHKLM). Together with the new data, we analyze the photometric observations of V1027 Cyg that we have obtained and published previously. Our search f...

We present the results of our $UBV$ and $JHKLM$-photometry for the semiregular pulsating variable V1027~Cyg, a supergiant with an infrared excess, over the period from 1991 to 2015. Our search for a periodicity in the $UBV$ brightness variations has led to several periods from $P=212^{d}$ to $P=320^{d}$ in different time intervals. We have found th...

This paper continues a study of the photometric activity of UX Ori stars in the optical and near-infrared (JHKLM bands) initiated in 2000. For comparison, the list of program stars contains two Herbig Ae stars that are photometrically quiet in the optical: MWC480 andHD179218. Fadings ofUXOri stars in the optical (V band) due to sporadic increases o...

The data of photometric measurements of the long-period eclipsing variable epsilon Aur in the two main minima 1982 and 2010 in the spectral range of 1--5 microns are presented. Noted is the similarity of light curves in eclipse, its asymmetry, and availability of the short interval increased brightness. We are detecting the phase changing of the in...

As a result of the next cycle of our long-term monitoring, we present our UBV JHKLM photometry for the symbiotic nova V1016 Cyg in 2008–2014. The star continued to systematically fade and redden in UBV: over this period, the brightness declined by 0ṃ1 in V and by 0ṃ2 in B and U, the B–V color index increased by 0ṃ1, and U–B barely changed. On the c...

FUor outbursts in young stellar objects (YSOs) are the most dramatic events among episodic accretion phenomena. The origin of these bursts is not clear: disk instabilities and/or disk perturbations by an external body being the most viable hypotheses. Here, we report our VLT/SINFONI high angular resolution AO-assisted observations of 2MASS J0659315...

Long-term JHKLM photometric measurements of the oxygen Mira variables RU Her and RS Vir are presented. Variations of the brightnesses and colors of these stars over the observation period are analyzed, and master light curves and color indices of these stars are derived. A linear trend was present in the mean infrared brightness of RS Vir on a time...

Long-term (1994-2014) near-infrared observations of P Cyg, kDra, and BUTau are analyzed. It is shown that the observed brightness and color variations in P Cyg and k Dra can be explained by variations in the parameters of the stars themselves and their ionized circumstellar shells, whose excitation requires from 5 to 15% of the star’s luminosity. T...

We investigate the correlation between infrared (JHKL) and optical (B) fluxes of the variable nucleus of the Seyfert galaxy NGC 4151 using partially published data for the last 6 years (2008-2013.). Here we are using the same data as in Oknyansky et al. (2014), but include also optical (B) data from Guo et al. We find that the lag of flux in all th...

Photometric data in the JHKLM near infrared bands obtained in 1999-2000 are presented for the long-period eclipsing system epsilon Aur. The time of secondary eclipse (when the F21 supergiant eclipses a dust disk surrounding the more massive component of the system) is calculated using the latest orbital elements of the system. A brightness minimum...

We investigate the correlation between infrared (JHKL) and optical (B) fluxes of the variable nucleus of the Seyfert galaxy NGC4151 using partially published data for the last 6 years (2008-2013). We find that the lag of flux in all the infrared bands is the same, 40 +/- 6 days, to within the measurement accuracy. Variability in the J and K bands i...

We present the results of our spectroscopic and photometric observations of the classical symbiotic star V1413 Aql obtained during different stages of its activity.

The results of JHKLM photometry for Nova Delphini 2013 obtained in the first sixty days after its outburst are analyzed. Analysis of the energy distribution in a wide spectral range (0.36–5 µm) has shown that the source mimics the emission of normal supergiants of spectral types B5 and A0 for two dates near its optical brightness maximum, August 15...

Long-term (1985–2013) JHKLM photometry for FG Sge is analyzed. Parameters of the supergiant and optical properties of the dust in the dust shell (DS) have been refined. Given the optical photometry, the spectral energy distribution of FG Sge at J brightness maxima in the range 1.25–5 µm is consistent with the classification of the supergiant as a K...

We analyze the results of our spectroscopic and photometric monitoring of V407 Cyg in 1984–2009. We show that the hot component of V407 Cyg can be in four different states: a passive state (the system looks as an ordinary, non-symbiotic Mira), a quiescent state (the system looks as a low-excitation classical symbiotic star), a Z And-type outburst,...

We present the result of the IR photometry of Nova Del 2013 obtained at the Crimean Station (Nauchny, Ukraine) of the Sternberg Astronomical Institute. JHKLM photometry was carried out with 125-cm telescope using a InSb-photometer on:

We analyze the results of our IR photometric monitoring of T CrB during 1987-2003 and describe the ellipsoidal variability of the Roche lobe filling cool component. We obtain limits to the binary inclination of i ∈ [50,60] deg and binary mass ratio q ∈ [0.4,2] (90 per cent confidence). The mass of the hot component is therefore 1.3-3 M⊙. If the hot...

We present the results of our infrared J H K L photometry of the Seyfert galaxy NGC 4151 during its active period in 1995–2011. The variable IR source was still in its active state in 2011, though its observed luminosity had almost halved compared to the maximum of 1995–1996. If the “cool” component of the galaxy’s variable source is a dust shell h...

We present the results of our photometric UBV JHKLM observations in 2008–2011 for the classical symbiotic star V1413 Aql. At the end of 2008, the hot component of V1413 Aql experienced the next strong outburst (ΔV > 2 ·m 5). According to the photometric criterion (B-V ≈ 0 ·m 9 ± 0 ·m 2), the star was in an active state even in the period preceding...

We have analyzed the activity of four UX Ori stars in the near-IR (JHKL) and visual (V) using the results of long-term photometric observations. For comparison, we also obtained IR (JHKLM) photometric observations of two visually quiet young stars of close spectral types (AB Aur and HD 190073). For the photometrically most active UX Ori stars BF Or...

Our JK photometry of Cyg X-1 was performed at the 1.25-m telescope of the Crimean Laboratory of the Sternberg Astronomical Institute using a photometer with a liquid-nitrogen-cooled InSb detector. The photometer was mounted at the Cassegrain focus of the telescope; the exit aperture was ~12". Observations were made between June, 1995 and September,...

The angular diameters, radii, and effective temperatures of 16 G0–G5 main-sequence stars with color excesses 0.60≤B-V≤0.68 and parallaxes derived from Hipparcos data have been determined using their infrared fluxes, obtained from JHKLM photometric observations. For all the stars except BS 483, these effective temperatures differ from the spectrosco...

We present the results of our analysis of the spectrophotometric and photometric data for the symbiotic nova PU Vul acquired in 2001–2008. The continuum in the optical observed in 2006–2008 cannot be reconciled with a standard model including light from the cool component, hot component, and nebula. The hot component’s temperature increased to 194...

We present the results of our infrared observations of WR 140 (=V1687 Cyg) in 2001–2010. Analysis of the observations has shown that the J brightness at maximum increased near the periastron by about 0 m .3; the M brightness increased by ∼2 m in less than 50 days. The minimum J brightness and the minimum L and M brightnesses were observed 550–600 a...

Long-term (1984–2008) JHKLM photometry for 254 objects is presented. The observations were carried out in the standard JHKLM photometric system using an original method and a modern IR photometer designed and built at the Sternberg Astronomical Institute. Our program of studies included searches for and studies of relatively hot circumstellar dust...

Our observations were carried out on the 125-cm telescope of the Crimean Laboratory of the Sternberg Astronomical Institute (SAI) of Moscow State University using a single-channel InSb photometer with a standard JHKLM photometric system. (4 data files).

The infrared photometry of WR140 (V1687 Cyg) was performed with the 1.25-m telescope at the Crimean Laboratory of the Sternberg Astronomical Institute using a photometer with a liquid-nitrogen-cooled photovoltaic indium antimonide (InSb) detector. (1 data file).

A Nova Source of Gamma Rays Novae are thermonuclear explosions that occur at the surface of a white dwarf when material is pulled onto it from a companion star in a binary system. They are different from supernovae because the explosion does not completely destroy the white dwarf. Novae have not been widely considered as high-energy gamma-ray sourc...

We present JHKLM photometry obtained in 1984–2009 for the RCB stars UV Cas and SU Tau. No major fadings characteristic of RCB stars were detected during the observations of UV Cas, while two events of this kind occurred for SU Tau. The observed flux and color-index variations can be explained with a changing dust concentration in the line of sight,...

We have analyzed our long-term (1995-2008) JHKLM photometry for three variable RV Tau supergiants. It follows from this analysis that: the amplitude of the JHK brightness variations is approximately the same, 0.9-1mag, for the three stars; a negative linear trend is noticeable in the variations of the mean J brightness for AC Her; and the mean J br...

We have analyzed our long-term (1995–2008) JHKLM photometry for three variable RV Tau supergiants. It follows from this analysis that: the amplitude of the JHK brightness variations is approximately the same, 0 m . 9–1 m , for the three stars; a negative linear trend is noticeable in the variations of the mean J brightness for AC Her; and the mean...

JHKLM photometry for two RV Tau stars (R Sge and RV Tau) and the yellow supergiant V1027 Cyg is analyzed.

The results of photometric measurements of the eclipsing variable \varepsilon Aur obtained in 1980-2009 in the 1-5 mum spectral range are presented. Observations in the 3.5-5 mum range exhibit an excess relative to the light from the F supergiant, which corresponds to emission from a cool source with temperature ˜ 400-1000 K. Neutral character of a...

We present the results of new UBVJHKL photometric and spectroscopic observations of the symbiotic nova PU Vul.

We present and discuss the results of our long-term JHKLM photometry for two RV Tau stars (R Sge and RV Tau) and the yellow supergiant V1027 Cyg, a candidate for protoplanetary nebulae. The amplitude of the infrared brightness variations in R Sge and RV Tau over fourteen years of observations was 0 .m 9−1m ; the infrared brightness variations in V1...

The behavior of DY Per during the latest deep decline event is studied on the basis of BVRIJHKLM photometry, low resolution near-infrared spectra and long-term photographic monitoring in red light. The relation of DY Per to RCB-type stars and to DY Per-like stars is discussed from the viewpoint of properties of their light variations. The spectral...

We combine all published and new unpublished yet NIR (near infrared) photometrical observations of NGC 4151 which can be used for determination of time delays between optical and NIR variations. In previous study we have found that the values of time delay in NIR filters are not the same for different states of the luminosity. Here we consider the...

We present the results of our long-term (about 13 years) J and K photometry of the X-ray binary Cyg X-1. The object's JK variability amplitudes were less than 0.2 mag. The J and K orbital light curves are appreciably asymmetric in quadratures. The secondary minimum is deeper, in comparison to the primary, and it is probable that the star becomes ho...

Our observations of Comet C/2004 Q2 (Machholz) in the range from 1.2 to 4.8 µm indicate that the material outflowed from the cometary surface in the form of fragments that separated into gas and dust under sublimation on time scales of the order of days. The albedo of these fragments in the range under study was wavelength independent, while the du...

We discuss the infrared (IR) (1.25-5microns) photometry of eight planetary nebulae performed in 1999-2006. For all of the nebulae under study, we have firmly established IR brightness and color variations on time scales shorter than one year and up to 6-8 years. The greatest IR brightness variations were observed in IC 2149, IC 4997, and NGC 7662....

We present the JHKLM photometry for 22 hot stars, 11 of which were identified in the GCVS. For all of the observed objects, we have estimated the interstellar reddening, angular diameters, and the volume emission measures of their gaseous shalls. (2 data files).

We discuss the infrared (IR) (1.25–5 µm) photometry of eight planetary nebulae performed in 1999–2006. For all of the nebulae under study, we have firmly established IR brightness and color variations on time scales shorter than one year and up to 6–8 years. The greatest IR brightness variations were observed in IC 2149, IC 4997, and NGC 7662. Thei...

Infrared observations of the unique symbiotic system CH Cyg in 2003–2006 are presented. Analysis of the observations has shown that a fairly dense dust structure (a cloud or a shell) appeared on the line of sight in August–November 2006. The dust grains in the new shell are similar in optical properties to graphite ones and their sizes are mostly w...

We analyze the results of new multicolor UBVRIJHKLM photometric observations of the symbiotic Mira V407 Cyg, obtained on return to quiescence from its 1998 outburst.

We combine all published NIR and optical photometric observations of NGC 4151 with our new yet unpublished data to determine the time delays between optical and NIR variations. Previously we have found changes in the time delay value for variations in the K and L filters for different states of the luminosity. Here we consider new data obtained dur...

Our 8-year-long JHKLM photometry of the Seyfert galaxy NGC 1068 has confirmed its IR variability. The amplitudes of the brightness variations in the J (1.25 µm) and K (2.2 µm) bands are within 0 . m 15 and 0 . m 3, respectively, and exceed the observational errors by more than a factor of 5. The nucleus of NGC 1068 is a variable source and can be a...

We present the results of JHKLM photometry of the oxygen Mira variable V2108 Oph acquired in 2000–2004. The period of brightness variations is refined (570 3 days), and light and color curves in the near-IR are presented. The mean fluxes, color temperatures, and sizes for two blackbodies representing the combined radiation of the star and dust shel...

We present the near-infrared speckle interferometry for LP And in the H and K' bands with diffraction-limited resolutions of 56 and 72 mas, new JHKLM photometry, and the results of our radiative transfer modelling of this carbon star. The reconstructed visibility reveals a spherically-symmetric envelope surrounding the central star. To determine th...

We discuss our JHKLM photometry for 22 hot stars, 11 of which were identified in the General Catalogue of Variable Stars. For all of the observed objects, we have estimated the interstellar reddening, angular diameters, and the volume emission measures of their gaseous shells.

We discuss the optical photometry of the classical symbiotic star BF Cyg obtained during the period 1978 2005 and analyse the eclipse of the active hot component in 1991.

We present the JHKLM photometry for five close (W Ser) binary systems obtained in the period 1996–2004. Positive phase shifts (with respect of the adopted ephemerides) have been found in the orbital infrared light curves for three binaries, RX Cas, KX And, and β Lyr; the rates of increase in their periods are ∼3.5 × 10−4, ∼1.6 × 10−3, and ∼1.4 × 10...

The infrared photometry of carbon stars was performed on the 1.25-m telescope at Crimean Station of the Sternberg Astronomical Institute. (2 data files).

We investigate the pulsation-phase dependent properties of the circumstellar dust shell (CDS) of the OH/IR star OH104.9+2.4 based on radiative transfer modeling (RTM) using the code DUSTY. Our previous study concerning simultaneous modeling of the spectral energy distribution (SED) and near-infrared (NIR) visibilities (Riechers et al. 2004) has now...

We present the results of our IR photometric observations of the classical symbiotic star BF Cyg acquired in 1978–2003. The variability range in the J and K bands was ∼0.2m. A periodic component in the cool star’s brightness variations is clearly visible, its period being half the orbital one and its J amplitude being ∼0.15m. This component is asso...

We combine all published NIR and optical photometrical observations of NGC 4151 as well as our new unpublished yet data which can be used for determination of time delays between optical and NIR variations. Before we have found change of time delay value for variations in K and L filters for different states of the luminosity. Here we are consideri...