## 1 Introduction  
Currently, electrochemical devices, such as supercapacitors, are increasingly used in various fields, where high pulse power is required for fairly short time intervals and high cyclic stability [1; 2; 3]. Examples of their application are hybrid electric vehicles, wind power structures or uninterruptible power supplies (UPS). In accordance with the charge accumulation mechanism, supercapacitors are usually divided into electric double layer capacitors (EDLC) and pseudocapacitors [4; 5]. The accumulation and conversion of energy into EDLC is carried out due to the separation of static charge in the Helmholtz layer. Various carbon materials (such as carbon black, activated carbon, few-layer graphene, etc.) are often used as the basis for the production of electrodes of this type of supercapacitors, providing a high speed of the charging and discharging process, as well as sufficient cyclic stability [5; 6; 7; 8; 9; 10; 11]. At the same time, their specific capacitance and energy density (<10 Wh/kg) are low [12]. Another type of supercapacitor is pseudocapacitors. The specific capacitance and energy density (20 Wh/kg and higher) of pseudocapacitors compared to EDLC can be significantly improved by reversible redox reactions (Faraday processes) on the surface or in the bulk of the electrode material [13]. Transition metal oxides [14; 15; 16] are commonly used as electrode materials for pseudocapacitors. Among transition metal oxides, manganese oxides are a very promising option, which have a high theoretical specific capacitance up to 1370 F/g, as well as low toxicity and production cost [17; 18]. There are several kinds of stable manganese oxide in nature: MnO (Mn(II) oxide), Mn\({}_{3}\)O\({}_{4}\) (Mn(II, III) oxide), Mn\({}_{2}\)O\({}_{3}\) (Mn(III) oxide), MnO\({}_{2}\) (Mn(IV) oxide) and Mn\({}_{2}\)O\({}_{7}\) (Mn(VII) oxide) [19; 20]. However, these materials have significant disadvantages when used as supercapacitor electrodes, namely: they are characterized by poor structural stability and low conductivity due to a significant change in volume during the charge-discharge process [21]. Therefore, different approaches are used to improve the stability of electrodes containing manganese oxide. One of these approaches is to apply Mn\({}_{x}\)O\({}_{y}\) (where x = 1, 2 or 3, and y = 1, 3 or 4) nanostructures to a carbon matrix, which has high conductivity, on the one hand, and high specific surface area and flexibility, on the other [22]. In this regard, it is advisable to use composite nanomaterials based on promising carbon materials (carbon nanotubes (CNTs) or graphene) and manganese oxide as the basis of pseudocapacitor electrodes, demonstrating their unique characteristics during energy storage and conversion [23; 24; 25; 26; 27; 28]. An analysis of the literature has shown that many works have been devoted to nanostructured materials based on MnO\({}_{2}\), while some electrode materials based on Mn\({}_{x}\)O\({}_{y}\) have great potential for use as supercapacitor materials, in particular, Mn\({}_{3}\)O\({}_{4}\)-based [29; 30; 21]. Moreover, as shown in [30; 31; 32; 33], annealing to 600 \({}^{\circ}\)C allows the transformation of amorphous or aqueous MnO\({}_{x}\) into Mn\({}_{2}\)O\({}_{3}\) or Mn\({}_{3}\)O\({}_{4}\) with a crystalline structure. It should be noted that in terms of the crystallinity of manganese oxide, the phase in which it is located, its distribution over the surface of the carbon matrix and interaction with it depend on the final capacitive characteristics of the electrode. Another interesting metal for supercapacitors is rhenium oxide, a metal belonging to the manganese group that has several oxidation states as manganese. In particular, it was shown in [34] that rhenium-modified activated carbon (AC) showed high values of specific capacitance (57 F/g at a discharge current of 0.2 A/g) and cyclic stability (more than 800 charge/discharge cycles).